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Chapter 49: Translations and Reflections

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Translations and Reflections in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Transformation (Transformation is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Translation (A translation slides a figure without turning or flipping it.)
  • Reflection (A reflection flips a figure across a line of reflection.)
  • Comparing image and original (Comparing image and original is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Real-life transformation problems (Real-life transformation problems is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

49.1 Transformation

Transformation is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Translate (2, 3) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (5, 1)

Worked Example 2

Problem: Translate (-1, 4) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (2, 2)

Worked Example 3

Problem: Translate (5, -2) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (8, -4)

Worked Example 4

Problem: Translate (0, 6) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (3, 4)

Worked Example 5

Problem: Translate (-3, -5) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (0, -7)

Worked Example 6

Problem: Translate (7, 1) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (10, -1)

Worked Example 7

Problem: Translate (-6, 2) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (-3, 0)

Worked Example 8

Problem: Translate (4, -7) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (7, -9)

Worked Example 9

Problem: Translate (1, 1) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (4, -1)

Worked Example 10

Problem: Translate (-2, 8) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (1, 6)

Practice Exercise

Create one new Grade 6 problem about Transformation. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.2 Translation

A translation slides a figure without turning or flipping it. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Translate (2, 3) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (5, 1)

Worked Example 2

Problem: Translate (-1, 4) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (2, 2)

Worked Example 3

Problem: Translate (5, -2) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (8, -4)

Worked Example 4

Problem: Translate (0, 6) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (3, 4)

Worked Example 5

Problem: Translate (-3, -5) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (0, -7)

Worked Example 6

Problem: Translate (7, 1) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (10, -1)

Worked Example 7

Problem: Translate (-6, 2) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (-3, 0)

Worked Example 8

Problem: Translate (4, -7) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (7, -9)

Worked Example 9

Problem: Translate (1, 1) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (4, -1)

Worked Example 10

Problem: Translate (-2, 8) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (1, 6)

Practice Exercise

Create one new Grade 6 problem about Translation. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.3 Translation on a grid

A translation slides a figure without turning or flipping it. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Translate (2, 3) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (5, 1)

Worked Example 2

Problem: Translate (-1, 4) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (2, 2)

Worked Example 3

Problem: Translate (5, -2) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (8, -4)

Worked Example 4

Problem: Translate (0, 6) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (3, 4)

Worked Example 5

Problem: Translate (-3, -5) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (0, -7)

Worked Example 6

Problem: Translate (7, 1) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (10, -1)

Worked Example 7

Problem: Translate (-6, 2) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (-3, 0)

Worked Example 8

Problem: Translate (4, -7) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (7, -9)

Worked Example 9

Problem: Translate (1, 1) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (4, -1)

Worked Example 10

Problem: Translate (-2, 8) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (1, 6)

Practice Exercise

Create one new Grade 6 problem about Translation on a grid. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.4 Translation rules with coordinates

A translation slides a figure without turning or flipping it. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant I

Worked Example 2

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant II

Worked Example 3

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant III

Worked Example 4

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant IV

Worked Example 5

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: on an axis

Worked Example 6

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: on an axis

Worked Example 7

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant II

Worked Example 8

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant IV

Worked Example 9

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant III

Worked Example 10

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant I

Practice Exercise

Create one new Grade 6 problem about Translation rules with coordinates. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.5 Reflection

A reflection flips a figure across a line of reflection. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Reflect (2, 3) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (2, -3)

Worked Example 2

Problem: Reflect (-1, 4) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-1, -4)

Worked Example 3

Problem: Reflect (5, -2) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (5, 2)

Worked Example 4

Problem: Reflect (0, 6) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (0, -6)

Worked Example 5

Problem: Reflect (-3, -5) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-3, 5)

Worked Example 6

Problem: Reflect (7, 1) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (7, -1)

Worked Example 7

Problem: Reflect (-6, 2) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-6, -2)

Worked Example 8

Problem: Reflect (4, -7) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (4, 7)

Worked Example 9

Problem: Reflect (1, 1) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (1, -1)

Worked Example 10

Problem: Reflect (-2, 8) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-2, -8)

Practice Exercise

Create one new Grade 6 problem about Reflection. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.6 Line of reflection

A reflection flips a figure across a line of reflection. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Reflect (2, 3) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (2, -3)

Worked Example 2

Problem: Reflect (-1, 4) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-1, -4)

Worked Example 3

Problem: Reflect (5, -2) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (5, 2)

Worked Example 4

Problem: Reflect (0, 6) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (0, -6)

Worked Example 5

Problem: Reflect (-3, -5) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-3, 5)

Worked Example 6

Problem: Reflect (7, 1) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (7, -1)

Worked Example 7

Problem: Reflect (-6, 2) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-6, -2)

Worked Example 8

Problem: Reflect (4, -7) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (4, 7)

Worked Example 9

Problem: Reflect (1, 1) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (1, -1)

Worked Example 10

Problem: Reflect (-2, 8) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-2, -8)

Practice Exercise

Create one new Grade 6 problem about Line of reflection. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.7 Reflection across a vertical line

A reflection flips a figure across a line of reflection. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Reflect (2, 3) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (2, -3)

Worked Example 2

Problem: Reflect (-1, 4) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-1, -4)

Worked Example 3

Problem: Reflect (5, -2) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (5, 2)

Worked Example 4

Problem: Reflect (0, 6) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (0, -6)

Worked Example 5

Problem: Reflect (-3, -5) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-3, 5)

Worked Example 6

Problem: Reflect (7, 1) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (7, -1)

Worked Example 7

Problem: Reflect (-6, 2) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-6, -2)

Worked Example 8

Problem: Reflect (4, -7) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (4, 7)

Worked Example 9

Problem: Reflect (1, 1) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (1, -1)

Worked Example 10

Problem: Reflect (-2, 8) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-2, -8)

Practice Exercise

Create one new Grade 6 problem about Reflection across a vertical line. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.8 Reflection across a horizontal line

A reflection flips a figure across a line of reflection. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Reflect (2, 3) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (2, -3)

Worked Example 2

Problem: Reflect (-1, 4) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-1, -4)

Worked Example 3

Problem: Reflect (5, -2) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (5, 2)

Worked Example 4

Problem: Reflect (0, 6) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (0, -6)

Worked Example 5

Problem: Reflect (-3, -5) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-3, 5)

Worked Example 6

Problem: Reflect (7, 1) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (7, -1)

Worked Example 7

Problem: Reflect (-6, 2) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-6, -2)

Worked Example 8

Problem: Reflect (4, -7) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (4, 7)

Worked Example 9

Problem: Reflect (1, 1) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (1, -1)

Worked Example 10

Problem: Reflect (-2, 8) across the x-axis.

  1. Keep x the same.
  2. Change the sign of y.

Very beginner explanation: A reflection across the x-axis reverses the vertical coordinate.

Answer: (-2, -8)

Practice Exercise

Create one new Grade 6 problem about Reflection across a horizontal line. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.9 Reflection across the x-axis

A reflection flips a figure across a line of reflection. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant I

Worked Example 2

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant II

Worked Example 3

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant III

Worked Example 4

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant IV

Worked Example 5

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: on an axis

Worked Example 6

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: on an axis

Worked Example 7

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant II

Worked Example 8

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant IV

Worked Example 9

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant III

Worked Example 10

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant I

Practice Exercise

Create one new Grade 6 problem about Reflection across the x-axis. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.10 Reflection across the y-axis

A reflection flips a figure across a line of reflection. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant I

Worked Example 2

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant II

Worked Example 3

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant III

Worked Example 4

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant IV

Worked Example 5

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: on an axis

Worked Example 6

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: on an axis

Worked Example 7

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant II

Worked Example 8

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant IV

Worked Example 9

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant III

Worked Example 10

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant I

Practice Exercise

Create one new Grade 6 problem about Reflection across the y-axis. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.11 Comparing image and original

Comparing image and original is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant I

Worked Example 2

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant II

Worked Example 3

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant III

Worked Example 4

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant IV

Worked Example 5

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: on an axis

Worked Example 6

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: on an axis

Worked Example 7

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant II

Worked Example 8

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant IV

Worked Example 9

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant III

Worked Example 10

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

  1. Read x first: move horizontally.
  2. Read y second: move vertically.
  3. Identify the quadrant or axis.

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

Answer: Quadrant I

Practice Exercise

Create one new Grade 6 problem about Comparing image and original. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

49.12 Real-life transformation problems

Real-life transformation problems is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Translate (2, 3) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (5, 1)

Worked Example 2

Problem: Translate (-1, 4) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (2, 2)

Worked Example 3

Problem: Translate (5, -2) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (8, -4)

Worked Example 4

Problem: Translate (0, 6) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (3, 4)

Worked Example 5

Problem: Translate (-3, -5) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (0, -7)

Worked Example 6

Problem: Translate (7, 1) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (10, -1)

Worked Example 7

Problem: Translate (-6, 2) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (-3, 0)

Worked Example 8

Problem: Translate (4, -7) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (7, -9)

Worked Example 9

Problem: Translate (1, 1) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (4, -1)

Worked Example 10

Problem: Translate (-2, 8) by (3, -2).

  1. Add 3 to x.
  2. Subtract 2 from y.

Very beginner explanation: A translation moves every point the same horizontal and vertical amounts.

Answer: (1, 6)

Practice Exercise

Create one new Grade 6 problem about Real-life transformation problems. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

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30 Review Questions and Answers

Q1. What is important to understand about Transformation?

Answer: Transformation is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q2. What is important to understand about Translation?

Answer: A translation slides a figure without turning or flipping it.

Q3. What is important to understand about Translation on a grid?

Answer: A translation slides a figure without turning or flipping it.

Q4. What is important to understand about Translation rules with coordinates?

Answer: A translation slides a figure without turning or flipping it.

Q5. What is important to understand about Reflection?

Answer: A reflection flips a figure across a line of reflection.

Q6. What is important to understand about Line of reflection?

Answer: A reflection flips a figure across a line of reflection.

Q7. What is important to understand about Reflection across a vertical line?

Answer: A reflection flips a figure across a line of reflection.

Q8. What is important to understand about Reflection across a horizontal line?

Answer: A reflection flips a figure across a line of reflection.

Q9. What is important to understand about Reflection across the x-axis?

Answer: A reflection flips a figure across a line of reflection.

Q10. What is important to understand about Reflection across the y-axis?

Answer: A reflection flips a figure across a line of reflection.

Q11. What is important to understand about Comparing image and original?

Answer: Comparing image and original is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Real-life transformation problems?

Answer: Real-life transformation problems is a Grade 6 mathematics idea in Translations and Reflections. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

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 final answer is reasonable before accepting it.

Q15. Why do units matter?

Answer: Units tell what a value measures and help 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, a table, or a second method.

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

Answer: Identify what is known, what is unknown, and the 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, operations, signs, units, rules, and calculations.

Q21. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q22. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q23. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q24. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q25. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q26. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q27. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q28. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q29. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.

Q30. What does representing mathematics mean?

Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.