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Chapter 41: Transformations and Dilations Review

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
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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.

41.1 Transformation

Transformation is an important Grade 8 concept in Transformations and Dilations Review. 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: Translate (2,3) by vector (3,-2).

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

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

Answer: (5,1)

Worked Example 2

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

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

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

Answer: (2,2)

Worked Example 3

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

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

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

Answer: (8,-4)

Worked Example 4

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

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

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

Answer: (3,4)

Worked Example 5

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

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

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

Answer: (0,-7)

Worked Example 6

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

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

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

Answer: (10,-1)

Worked Example 7

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

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

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

Answer: (-3,0)

Worked Example 8

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

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

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

Answer: (7,-9)

Worked Example 9

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

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

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

Answer: (4,-1)

Worked Example 10

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

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

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

Answer: (1,6)

Practice exercise

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

41.2 Translation

A translation slides every point of a figure the same distance in the same direction. In this section, the focus is Translation.

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

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

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

Answer: (5,1)

Worked Example 2

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

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

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

Answer: (2,2)

Worked Example 3

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

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

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

Answer: (8,-4)

Worked Example 4

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

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

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

Answer: (3,4)

Worked Example 5

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

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

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

Answer: (0,-7)

Worked Example 6

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

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

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

Answer: (10,-1)

Worked Example 7

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

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

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

Answer: (-3,0)

Worked Example 8

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

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

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

Answer: (7,-9)

Worked Example 9

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

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

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

Answer: (4,-1)

Worked Example 10

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

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

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

Answer: (1,6)

Practice exercise

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

41.3 Reflection

A reflection flips a figure across a line of reflection. In this section, the focus is Reflection.

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

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

Very beginner explanation: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

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: Reflecting across the x-axis changes vertical position but not horizontal position.

Answer: (-2,-8)

Practice exercise

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

41.4 Rotation

A rotation turns a figure around a fixed centre. In this section, the focus is Rotation.

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: Rotate (2,3) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-3,2)

Worked Example 2

Problem: Rotate (-1,4) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-4,-1)

Worked Example 3

Problem: Rotate (5,-2) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (2,5)

Worked Example 4

Problem: Rotate (0,6) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-6,0)

Worked Example 5

Problem: Rotate (-3,-5) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (5,-3)

Worked Example 6

Problem: Rotate (7,1) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-1,7)

Worked Example 7

Problem: Rotate (-6,2) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-2,-6)

Worked Example 8

Problem: Rotate (4,-7) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (7,4)

Worked Example 9

Problem: Rotate (1,1) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-1,1)

Worked Example 10

Problem: Rotate (-2,8) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-8,-2)

Practice exercise

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

41.5 Dilation

A dilation enlarges or reduces a figure using a scale factor while preserving shape. In this section, the focus is Dilation.

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: Dilate (2,3) from the origin by scale factor 2.

  1. Multiply both coordinates by the scale factor.
  2. x': 2×2; y': 3×2.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (4,6)

Worked Example 2

Problem: Dilate (-1,4) from the origin by scale factor 0.5.

  1. Multiply both coordinates by the scale factor.
  2. x': -1×0.5; y': 4×0.5.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (-0.5,2)

Worked Example 3

Problem: Dilate (5,-2) from the origin by scale factor 3.

  1. Multiply both coordinates by the scale factor.
  2. x': 5×3; y': -2×3.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (15,-6)

Worked Example 4

Problem: Dilate (0,6) from the origin by scale factor 1.5.

  1. Multiply both coordinates by the scale factor.
  2. x': 0×1.5; y': 6×1.5.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (0,9)

Worked Example 5

Problem: Dilate (-3,-5) from the origin by scale factor 0.25.

  1. Multiply both coordinates by the scale factor.
  2. x': -3×0.25; y': -5×0.25.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (-0.75,-1.25)

Worked Example 6

Problem: Dilate (7,1) from the origin by scale factor 2.

  1. Multiply both coordinates by the scale factor.
  2. x': 7×2; y': 1×2.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (14,2)

Worked Example 7

Problem: Dilate (-6,2) from the origin by scale factor 0.5.

  1. Multiply both coordinates by the scale factor.
  2. x': -6×0.5; y': 2×0.5.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (-3,1)

Worked Example 8

Problem: Dilate (4,-7) from the origin by scale factor 3.

  1. Multiply both coordinates by the scale factor.
  2. x': 4×3; y': -7×3.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (12,-21)

Worked Example 9

Problem: Dilate (1,1) from the origin by scale factor 1.5.

  1. Multiply both coordinates by the scale factor.
  2. x': 1×1.5; y': 1×1.5.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (1.5,1.5)

Worked Example 10

Problem: Dilate (-2,8) from the origin by scale factor 0.25.

  1. Multiply both coordinates by the scale factor.
  2. x': -2×0.25; y': 8×0.25.

Very beginner explanation: A dilation from the origin multiplies both coordinates by the same scale factor.

Answer: (-0.5,2)

Practice exercise

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

41.6 Centre of rotation

A rotation turns a figure around a fixed centre. In this section, the focus is Centre of rotation.

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: Rotate (2,3) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-3,2)

Worked Example 2

Problem: Rotate (-1,4) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-4,-1)

Worked Example 3

Problem: Rotate (5,-2) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (2,5)

Worked Example 4

Problem: Rotate (0,6) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-6,0)

Worked Example 5

Problem: Rotate (-3,-5) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (5,-3)

Worked Example 6

Problem: Rotate (7,1) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-1,7)

Worked Example 7

Problem: Rotate (-6,2) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-2,-6)

Worked Example 8

Problem: Rotate (4,-7) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (7,4)

Worked Example 9

Problem: Rotate (1,1) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-1,1)

Worked Example 10

Problem: Rotate (-2,8) 90° counterclockwise about the origin.

  1. Use the rule (x,y) → (-y,x).

Very beginner explanation: A 90° counterclockwise rotation swaps the coordinates and changes the sign of the old y-value.

Answer: (-8,-2)

Practice exercise

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

41.7 Line of reflection

A reflection flips a figure across a line of reflection. In this section, the focus is Line of reflection.

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 Line of reflection. Show the important steps, include units when needed, and explain how you checked the answer.

41.8 Scale factor in dilation

A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Scale factor in dilation.

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: An original length is 6 cm and the scale factor is 0.5. Find the image length.

  1. Multiply the original by 0.5.
  2. 6 × 0.5 = 3.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 3 cm

Worked Example 2

Problem: An original length is 10 cm and the scale factor is 1.5. Find the image length.

  1. Multiply the original by 1.5.
  2. 10 × 1.5 = 15.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 15 cm

Worked Example 3

Problem: An original length is 17 cm and the scale factor is 2. Find the image length.

  1. Multiply the original by 2.
  2. 17 × 2 = 34.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 34 cm

Worked Example 4

Problem: An original length is 23 cm and the scale factor is 2.5. Find the image length.

  1. Multiply the original by 2.5.
  2. 23 × 2.5 = 57.5.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 57.5 cm

Worked Example 5

Problem: An original length is 20 cm and the scale factor is 3. Find the image length.

  1. Multiply the original by 3.
  2. 20 × 3 = 60.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 60 cm

Worked Example 6

Problem: An original length is 14 cm and the scale factor is 0.5. Find the image length.

  1. Multiply the original by 0.5.
  2. 14 × 0.5 = 7.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 7 cm

Worked Example 7

Problem: An original length is 11 cm and the scale factor is 1.5. Find the image length.

  1. Multiply the original by 1.5.
  2. 11 × 1.5 = 16.5.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 16.5 cm

Worked Example 8

Problem: An original length is 18 cm and the scale factor is 2. Find the image length.

  1. Multiply the original by 2.
  2. 18 × 2 = 36.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 36 cm

Worked Example 9

Problem: An original length is 27 cm and the scale factor is 2.5. Find the image length.

  1. Multiply the original by 2.5.
  2. 27 × 2.5 = 67.5.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 67.5 cm

Worked Example 10

Problem: An original length is 16 cm and the scale factor is 3. Find the image length.

  1. Multiply the original by 3.
  2. 16 × 3 = 48.

Very beginner explanation: A scale factor multiplies every corresponding length by the same number.

Answer: 48 cm

Practice exercise

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

41.9 Coordinates after translation

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

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 Coordinates after translation. Show the important steps, include units when needed, and explain how you checked the answer.

41.10 Coordinates after reflection

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

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 Coordinates after reflection. Show the important steps, include units when needed, and explain how you checked the answer.

41.11 Coordinates after rotation

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

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 Coordinates after rotation. Show the important steps, include units when needed, and explain how you checked the answer.

41.12 Coordinates after dilation

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

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 Coordinates after dilation. Show the important steps, include units when needed, and explain how you checked the answer.

41.13 Combining transformations

Combining transformations is an important Grade 8 concept in Transformations and Dilations Review. 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: Translate (2,3) by vector (3,-2).

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

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

Answer: (5,1)

Worked Example 2

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

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

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

Answer: (2,2)

Worked Example 3

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

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

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

Answer: (8,-4)

Worked Example 4

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

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

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

Answer: (3,4)

Worked Example 5

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

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

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

Answer: (0,-7)

Worked Example 6

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

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

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

Answer: (10,-1)

Worked Example 7

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

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

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

Answer: (-3,0)

Worked Example 8

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

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

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

Answer: (7,-9)

Worked Example 9

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

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

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

Answer: (4,-1)

Worked Example 10

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

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

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

Answer: (1,6)

Practice exercise

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

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Chapter 41 Review Questions and Answers

Q1. What is important to remember about Transformation?

Answer: Transformation is an important Grade 8 concept in Transformations and Dilations Review. 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 Translation?

Answer: A translation slides every point of a figure the same distance in the same direction. In this section, the focus is Translation.

Q3. What is important to remember about Reflection?

Answer: A reflection flips a figure across a line of reflection. In this section, the focus is Reflection.

Q4. What is important to remember about Rotation?

Answer: A rotation turns a figure around a fixed centre. In this section, the focus is Rotation.

Q5. What is important to remember about Dilation?

Answer: A dilation enlarges or reduces a figure using a scale factor while preserving shape. In this section, the focus is Dilation.

Q6. What is important to remember about Centre of rotation?

Answer: A rotation turns a figure around a fixed centre. In this section, the focus is Centre of rotation.

Q7. What is important to remember about Line of reflection?

Answer: A reflection flips a figure across a line of reflection. In this section, the focus is Line of reflection.

Q8. What is important to remember about Scale factor in dilation?

Answer: A factor (a whole number that divides another number exactly) helps with simplifying fractions and finding common group sizes. In this section, the focus is Scale factor in dilation.

Q9. What is important to remember about Coordinates after translation?

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 Coordinates after translation.

Q10. What is important to remember about Coordinates after reflection?

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 Coordinates after reflection.

Q11. What is important to remember about Coordinates after rotation?

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 Coordinates after rotation.

Q12. What is important to remember about Coordinates after dilation?

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 Coordinates after dilation.

Q13. What is important to remember about Combining transformations?

Answer: Combining transformations is an important Grade 8 concept in Transformations and Dilations Review. 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.

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.