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Chapter 48: Coordinate Geometry and Distance

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 12 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.

48.1 Horizontal distance

Horizontal distance is an important Grade 8 concept in Coordinate Geometry and Distance. 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 distance. Show the important steps, include units when needed, and explain how you checked the answer.

48.2 Vertical distance

Vertical distance is an important Grade 8 concept in Coordinate Geometry and Distance. 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 Vertical distance. Show the important steps, include units when needed, and explain how you checked the answer.

48.3 Distance on a number line

Distance on a number line is an important Grade 8 concept in Coordinate Geometry and Distance. 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 Distance on a number line. Show the important steps, include units when needed, and explain how you checked the answer.

48.4 Right triangles on a coordinate grid

Coordinates locate a point using an ordered pair (x, y), with horizontal movement first and vertical movement second. In this section, the focus is Right triangles on a coordinate grid.

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: A triangle has angles 35° and 45°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-35-45=100.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 100°

Worked Example 2

Problem: A triangle has angles 48° and 58°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-48-58=74.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 74°

Worked Example 3

Problem: A triangle has angles 67° and 47°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-67-47=66.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 66°

Worked Example 4

Problem: A triangle has angles 72° and 52°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-72-52=56.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 56°

Worked Example 5

Problem: A triangle has angles 110° and 60°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-110-60=10.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 10°

Worked Example 6

Problem: A triangle has angles 25° and 65°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-25-65=90.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 90°

Worked Example 7

Problem: A triangle has angles 58° and 68°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-58-68=54.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 54°

Worked Example 8

Problem: A triangle has angles 83° and 63°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-83-63=34.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 34°

Worked Example 9

Problem: A triangle has angles 95° and 45°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-95-45=40.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 40°

Worked Example 10

Problem: A triangle has angles 120° and 40°. Find the third angle.

  1. Triangle interior angles total 180°.
  2. 180-120-40=20.

Very beginner explanation: Subtract the known angles from 180°.

Answer: 20°

Practice exercise

Create one new Grade 8 problem involving Right triangles on a coordinate grid. Show the important steps, include units when needed, and explain how you checked the answer.

48.5 Pythagorean distance

The Pythagorean theorem relates the side lengths of a right triangle: a² + b² = c², where c is the hypotenuse. In this section, the focus is Pythagorean distance.

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 Pythagorean distance. Show the important steps, include units when needed, and explain how you checked the answer.

48.6 Finding missing coordinates introduction

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

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 Finding missing coordinates introduction. Show the important steps, include units when needed, and explain how you checked the answer.

48.7 Midpoints review

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

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 midpoint between 35 and 45 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 40

Worked Example 2

Problem: Find the midpoint between 48 and 58 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 53

Worked Example 3

Problem: Find the midpoint between 67 and 77 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 72

Worked Example 4

Problem: Find the midpoint between 72 and 82 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 77

Worked Example 5

Problem: Find the midpoint between 110 and 120 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 115

Worked Example 6

Problem: Find the midpoint between 25 and 35 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 30

Worked Example 7

Problem: Find the midpoint between 58 and 68 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 63

Worked Example 8

Problem: Find the midpoint between 83 and 93 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 88

Worked Example 9

Problem: Find the midpoint between 95 and 105 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 100

Worked Example 10

Problem: Find the midpoint between 120 and 130 on a number line.

  1. Add the endpoints.
  2. Divide by 2.

Very beginner explanation: The midpoint is exactly halfway between two endpoints.

Answer: 125

Practice exercise

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

48.8 Graphing geometric figures

The metric system is a base-10 measurement system used for length, mass, capacity, area, and volume. In this section, the focus is Graphing geometric figures.

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 Graphing geometric figures. Show the important steps, include units when needed, and explain how you checked the answer.

48.9 Perimeter on a coordinate grid

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

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 perimeter of a rectangle 5 cm by 2 cm.

  1. Use P = 2(l+w).
  2. P = 2(5+2).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 14 cm

Worked Example 2

Problem: Find the perimeter of a rectangle 6 cm by 3 cm.

  1. Use P = 2(l+w).
  2. P = 2(6+3).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 18 cm

Worked Example 3

Problem: Find the perimeter of a rectangle 7 cm by 4 cm.

  1. Use P = 2(l+w).
  2. P = 2(7+4).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 22 cm

Worked Example 4

Problem: Find the perimeter of a rectangle 8 cm by 5 cm.

  1. Use P = 2(l+w).
  2. P = 2(8+5).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 26 cm

Worked Example 5

Problem: Find the perimeter of a rectangle 9 cm by 6 cm.

  1. Use P = 2(l+w).
  2. P = 2(9+6).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 30 cm

Worked Example 6

Problem: Find the perimeter of a rectangle 10 cm by 7 cm.

  1. Use P = 2(l+w).
  2. P = 2(10+7).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 34 cm

Worked Example 7

Problem: Find the perimeter of a rectangle 11 cm by 8 cm.

  1. Use P = 2(l+w).
  2. P = 2(11+8).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 38 cm

Worked Example 8

Problem: Find the perimeter of a rectangle 12 cm by 9 cm.

  1. Use P = 2(l+w).
  2. P = 2(12+9).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 42 cm

Worked Example 9

Problem: Find the perimeter of a rectangle 13 cm by 10 cm.

  1. Use P = 2(l+w).
  2. P = 2(13+10).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 46 cm

Worked Example 10

Problem: Find the perimeter of a rectangle 14 cm by 11 cm.

  1. Use P = 2(l+w).
  2. P = 2(14+11).

Very beginner explanation: Perimeter is the total distance around the outside of a figure.

Answer: 50 cm

Practice exercise

Create one new Grade 8 problem involving Perimeter on a coordinate grid. Show the important steps, include units when needed, and explain how you checked the answer.

48.10 Area on a coordinate grid

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

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 area of a rectangle 6 cm by 3 cm.

  1. Use A = length × width.
  2. A = 6×3.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 18 cm²

Worked Example 2

Problem: Find the area of a rectangle 7 cm by 4 cm.

  1. Use A = length × width.
  2. A = 7×4.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 28 cm²

Worked Example 3

Problem: Find the area of a rectangle 8 cm by 5 cm.

  1. Use A = length × width.
  2. A = 8×5.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 40 cm²

Worked Example 4

Problem: Find the area of a rectangle 9 cm by 6 cm.

  1. Use A = length × width.
  2. A = 9×6.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 54 cm²

Worked Example 5

Problem: Find the area of a rectangle 10 cm by 7 cm.

  1. Use A = length × width.
  2. A = 10×7.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 70 cm²

Worked Example 6

Problem: Find the area of a rectangle 11 cm by 8 cm.

  1. Use A = length × width.
  2. A = 11×8.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 88 cm²

Worked Example 7

Problem: Find the area of a rectangle 12 cm by 9 cm.

  1. Use A = length × width.
  2. A = 12×9.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 108 cm²

Worked Example 8

Problem: Find the area of a rectangle 13 cm by 10 cm.

  1. Use A = length × width.
  2. A = 13×10.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 130 cm²

Worked Example 9

Problem: Find the area of a rectangle 14 cm by 11 cm.

  1. Use A = length × width.
  2. A = 14×11.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 154 cm²

Worked Example 10

Problem: Find the area of a rectangle 15 cm by 12 cm.

  1. Use A = length × width.
  2. A = 15×12.

Very beginner explanation: Area measures the space inside a 2D figure and uses square units.

Answer: 180 cm²

Practice exercise

Create one new Grade 8 problem involving Area on a coordinate grid. Show the important steps, include units when needed, and explain how you checked the answer.

48.11 Real-life map problems

Real-life map problems is an important Grade 8 concept in Coordinate Geometry and Distance. 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: Real-life map problems: Explain Real-life map problems in one simple sentence.

  1. Look at the words in “Real-life map 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: Real-life map problems is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: Real-life map problems: A student says, “I can use Real-life map 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: Real-life map problems: What is the first step when solving a problem about Real-life map 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: Real-life map problems: After solving a Real-life map 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: Real-life map problems: Give one way Real-life map 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: Real-life map problems can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: Real-life map problems: Which representation could help explain Real-life map 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: Real-life map problems: A student gets an answer for Real-life map 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: Real-life map problems: Why can estimation help before a detailed Real-life map 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: Real-life map problems: How can you test whether your rule for Real-life map 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: Real-life map problems: How would you teach Real-life map 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 Real-life map problems. Show the important steps, include units when needed, and explain how you checked the answer.

48.12 Multi-step coordinate 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 Multi-step coordinate 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: Multi-step coordinate problems: Explain Multi-step coordinate problems in one simple sentence.

  1. Look at the words in “Multi-step coordinate 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: Multi-step coordinate problems is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: Multi-step coordinate problems: A student says, “I can use Multi-step coordinate 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: Multi-step coordinate problems: What is the first step when solving a problem about Multi-step coordinate 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: Multi-step coordinate problems: After solving a Multi-step coordinate 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: Multi-step coordinate problems: Give one way Multi-step coordinate 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: Multi-step coordinate problems can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: Multi-step coordinate problems: Which representation could help explain Multi-step coordinate 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: Multi-step coordinate problems: A student gets an answer for Multi-step coordinate 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: Multi-step coordinate problems: Why can estimation help before a detailed Multi-step coordinate 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: Multi-step coordinate problems: How can you test whether your rule for Multi-step coordinate 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: Multi-step coordinate problems: How would you teach Multi-step coordinate 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 Multi-step coordinate problems. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 48 Review Questions and Answers

Q1. What is important to remember about Horizontal distance?

Answer: Horizontal distance is an important Grade 8 concept in Coordinate Geometry and Distance. 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 Vertical distance?

Answer: Vertical distance is an important Grade 8 concept in Coordinate Geometry and Distance. 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 Distance on a number line?

Answer: Distance on a number line is an important Grade 8 concept in Coordinate Geometry and Distance. 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 Right triangles on a coordinate grid?

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 Right triangles on a coordinate grid.

Q5. What is important to remember about Pythagorean distance?

Answer: The Pythagorean theorem relates the side lengths of a right triangle: a² + b² = c², where c is the hypotenuse. In this section, the focus is Pythagorean distance.

Q6. What is important to remember about Finding missing coordinates introduction?

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 Finding missing coordinates introduction.

Q7. What is important to remember about Midpoints review?

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

Q8. What is important to remember about Graphing geometric figures?

Answer: The metric system is a base-10 measurement system used for length, mass, capacity, area, and volume. In this section, the focus is Graphing geometric figures.

Q9. What is important to remember about Perimeter on a coordinate grid?

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 Perimeter on a coordinate grid.

Q10. What is important to remember about Area on a coordinate grid?

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 Area on a coordinate grid.

Q11. What is important to remember about Real-life map problems?

Answer: Real-life map problems is an important Grade 8 concept in Coordinate Geometry and Distance. 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.

Q12. What is important to remember about Multi-step coordinate 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 Multi-step coordinate problems.

Q13. Why should you show your steps?

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

Q14. Why is estimation useful?

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

Q15. Why do units matter?

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

Q16. When should you round?

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

Q17. How can you check an answer?

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

Q18. What should you identify first in a word problem?

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

Q19. What makes a final answer complete?

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

Q20. What should you do if an answer seems unreasonable?

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

Q21. Why are diagrams useful?

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

Q22. Why are tables useful?

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

Q23. Why should you explain your reasoning?

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

Q24. How do mistakes help learning?

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

Q25. When is a calculator useful?

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

Q26. Why compare more than one strategy?

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

Q27. What is mathematical communication?

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

Q28. What is mathematical modelling?

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

Q29. Why should assumptions be stated?

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

Q30. Why should data sources be checked?

Answer: Reliable sources and fair collection methods make conclusions more trustworthy.