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Chapter 25: Coordinate Plane and Ordered Pairs

Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.

Grade 8Beginner Friendly5+ Examples Per TopicPractice30 Q&A
Estimated reading time0% read
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What this chapter covers

This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

25.1 Cartesian plane

Cartesian plane is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Cartesian plane. Show the important steps, include units when needed, and explain how you checked the answer.

25.2 x-axis

x-axis is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving x-axis. Show the important steps, include units when needed, and explain how you checked the answer.

25.3 y-axis

y-axis is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving y-axis. Show the important steps, include units when needed, and explain how you checked the answer.

25.4 Origin

Origin is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Origin. Show the important steps, include units when needed, and explain how you checked the answer.

25.5 Ordered pairs

Ordered pairs is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Ordered pairs. Show the important steps, include units when needed, and explain how you checked the answer.

25.6 Quadrant I

Quadrant I is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Quadrant I. Show the important steps, include units when needed, and explain how you checked the answer.

25.7 Quadrant II

Quadrant II is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Quadrant II. Show the important steps, include units when needed, and explain how you checked the answer.

25.8 Quadrant III

Quadrant III is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Quadrant III. Show the important steps, include units when needed, and explain how you checked the answer.

25.9 Quadrant IV

Quadrant IV is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Quadrant IV. Show the important steps, include units when needed, and explain how you checked the answer.

25.10 Plotting points

A point represents an exact location and has no length, width, or height. In this section, the focus is Plotting points.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Plotting points. Show the important steps, include units when needed, and explain how you checked the answer.

25.11 Reading coordinates

Coordinates locate a point using an ordered pair (x, y), with horizontal movement first and vertical movement second. In this section, the focus is Reading coordinates.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Reading coordinates. Show the important steps, include units when needed, and explain how you checked the answer.

25.12 Horizontal and vertical distance

Horizontal and vertical distance is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the supplementary angle to 35°.

  1. Supplementary angles total 180°.
  2. 180° - 35° = 145°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 145°

Worked Example 2

Problem: Find the supplementary angle to 48°.

  1. Supplementary angles total 180°.
  2. 180° - 48° = 132°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 132°

Worked Example 3

Problem: Find the supplementary angle to 67°.

  1. Supplementary angles total 180°.
  2. 180° - 67° = 113°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 113°

Worked Example 4

Problem: Find the supplementary angle to 72°.

  1. Supplementary angles total 180°.
  2. 180° - 72° = 108°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 108°

Worked Example 5

Problem: Find the supplementary angle to 110°.

  1. Supplementary angles total 180°.
  2. 180° - 110° = 70°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 70°

Worked Example 6

Problem: Find the supplementary angle to 25°.

  1. Supplementary angles total 180°.
  2. 180° - 25° = 155°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 155°

Worked Example 7

Problem: Find the supplementary angle to 58°.

  1. Supplementary angles total 180°.
  2. 180° - 58° = 122°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 122°

Worked Example 8

Problem: Find the supplementary angle to 83°.

  1. Supplementary angles total 180°.
  2. 180° - 83° = 97°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 97°

Worked Example 9

Problem: Find the supplementary angle to 95°.

  1. Supplementary angles total 180°.
  2. 180° - 95° = 85°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 85°

Worked Example 10

Problem: Find the supplementary angle to 120°.

  1. Supplementary angles total 180°.
  2. 180° - 120° = 60°.

Very beginner explanation: Angles on a straight line are supplementary.

Answer: 60°

Practice exercise

Create one new Grade 8 problem involving Horizontal and vertical distance. Show the important steps, include units when needed, and explain how you checked the answer.

25.13 Coordinate word problems

Coordinates locate a point using an ordered pair (x, y), with horizontal movement first and vertical movement second. In this section, the focus is Coordinate word problems.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Coordinate word problems: Explain Coordinate word problems in one simple sentence.

  1. Look at the words in “Coordinate word problems”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: Coordinate word problems is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: Coordinate word problems: A student says, “I can use Coordinate word problems without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: Coordinate word problems: What is the first step when solving a problem about Coordinate word problems?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: Coordinate word problems: After solving a Coordinate word problems problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: Coordinate word problems: Give one way Coordinate word problems could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: Coordinate word problems can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: Coordinate word problems: Which representation could help explain Coordinate word problems: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: Coordinate word problems: A student gets an answer for Coordinate word problems but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: Coordinate word problems: Why can estimation help before a detailed Coordinate word problems calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: Coordinate word problems: How can you test whether your rule for Coordinate word problems works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: Coordinate word problems: How would you teach Coordinate word problems to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving Coordinate word problems. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 25 Review Questions and Answers

Q1. What is important to remember about Cartesian plane?

Answer: Cartesian plane is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q2. What is important to remember about x-axis?

Answer: x-axis is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q3. What is important to remember about y-axis?

Answer: y-axis is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q4. What is important to remember about Origin?

Answer: Origin is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q5. What is important to remember about Ordered pairs?

Answer: Ordered pairs is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q6. What is important to remember about Quadrant I?

Answer: Quadrant I is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q7. What is important to remember about Quadrant II?

Answer: Quadrant II is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q8. What is important to remember about Quadrant III?

Answer: Quadrant III is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Quadrant IV?

Answer: Quadrant IV is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q10. What is important to remember about Plotting points?

Answer: A point represents an exact location and has no length, width, or height. In this section, the focus is Plotting points.

Q11. What is important to remember about Reading coordinates?

Answer: Coordinates locate a point using an ordered pair (x, y), with horizontal movement first and vertical movement second. In this section, the focus is Reading coordinates.

Q12. What is important to remember about Horizontal and vertical distance?

Answer: Horizontal and vertical distance is an important Grade 8 concept in Coordinate Plane and Ordered Pairs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q13. What is important to remember about Coordinate word problems?

Answer: Coordinates locate a point using an ordered pair (x, y), with horizontal movement first and vertical movement second. In this section, the focus is Coordinate word problems.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a calculated answer is reasonable.

Q16. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.

Q23. Why are tables useful?

Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.

Q24. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer was obtained.

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.

Q26. When is a calculator useful?

Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.

Q27. Why compare more than one strategy?

Answer: Different strategies may make a problem easier and provide a way to verify the result.

Q28. What is mathematical communication?

Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.

Q29. What is mathematical modelling?

Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.

Q30. Why should assumptions be stated?

Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.