Answer Keys: Transformations

Student Concept Worksheet Answers

1

P' = (7, -7)

P(5, -3) translated 2 right (+2 to x) and 4 down (-4 to y): (5+2, -3-4) = (7, -7)

2

Q' = (2, 6)

Q(-2, 6) reflected over y-axis: x changes sign, y stays same. (-2, 6) becomes (2, 6)

3

R' = (2, 4)

R(4, -2) rotated 90° CCW: (x, y) → (-y, x). So (4, -2) → (2, 4)

4

S' = (-6, 12)

S(-3, 6) dilated by scale factor 2: multiply both coordinates by 2. (-3×2, 6×2) = (-6, 12)

5

Congruent

Both translation and reflection are rigid transformations that preserve size and shape.

Practice Worksheet Answers

Part A: Translations

#	Answer	Work
1	A' = (1, 7)	(4-3, 2+5) = (1, 7)
2	B' = (3, 4)	(-1+4, 6-2) = (3, 4)
3	C' = (-5, -6)	(0-5, -3-3) = (-5, -6)
4	D' = (2, -3)	(-5+7, -4+1) = (2, -3)

Part B: Reflections

#	Answer	Work
5	E' = (3, 5)	Over x-axis: y changes sign. (3, -5) → (3, 5)
6	F' = (4, 2)	Over y-axis: x changes sign. (-4, 2) → (4, 2)
7	G' = (-6, -1)	Over y-axis: x changes sign. (6, -1) → (-6, -1)
8	H' = (-2, 7)	Over x-axis: y changes sign. (-2, -7) → (-2, 7)

Part C: Rotations

#	Answer	Work
9	I' = (-5, 2)	90° CCW: (x, y) → (-y, x). (2, 5) → (-5, 2)
10	J' = (3, -4)	180°: (x, y) → (-x, -y). (-3, 4) → (3, -4)
11	K' = (-6, -1)	90° CW: (x, y) → (y, -x). (1, -6) → (-6, -1)
12	L' = (-2, 4)	270° CCW = 90° CW: (x, y) → (y, -x). (-4, -2) → (-2, 4)

Part D: Dilations

#	Answer	Work
13	M' = (12, -6)	(4×3, -2×3) = (12, -6)
14	N' = (-3, 4)	(-6×0.5, 8×0.5) = (-3, 4)

Part E: Identify Transformations

#	Answer	Explanation
15	Reflection over x-axis	Only y changed sign: (3, 4) → (3, -4)
16	Rotation 90° CCW	(x, y) → (-y, x): (2, 5) → (-5, 2)
17	Translation 3 left, 4 up	(-1-3, 3+4) = (-4, 7) ✓
18	Dilation, scale factor 3	(4×3, 2×3) = (12, 6)

Part F: Sequences

19

P' = (2, -3), P'' = (-2, -3)

Reflect (2, 3) over x-axis: (2, -3). Then translate 4 left: (2-4, -3) = (-2, -3)

20

Q' = (-4, -1), Q'' = (4, -1)

Rotate (-1, 4) 90° CCW: (-4, -1). Then reflect over y-axis: (4, -1)

21

Congruent

Both translation and reflection are rigid transformations - they preserve size and shape.

22

Similar (not congruent)

Dilation changes size, so the final image is similar but not congruent to the original.

Challenge Questions:

#23: Rotation 180° about the origin. Reflecting over x-axis then y-axis: (a, b) → (a, -b) → (-a, -b), which is the same as 180° rotation.

#24: The area increases by a factor of 4 (the square of the scale factor). If scale factor = 2, area multiplies by 2² = 4. Original area = 4, new area = 16.

FAST Practice Quiz Answers

1

B) (-3, -2)

Reflect over y-axis: x changes sign, y stays same. (3, -2) → (-3, -2)

2

B) (-5, -4)

90° CCW: (x, y) → (-y, x). (-4, 5) → (-5, -4)

3

B) (6, -3)

Dilation by 3: (2×3, -1×3) = (6, -3)

4

Select: Translation, Reflection, Rotation

Translation 5 units left - YES (rigid)
Dilation scale factor 2 - NO (changes size)
Reflection over x-axis - YES (rigid)
Rotation 180° - YES (rigid)
Dilation scale factor 1/2 - NO (changes size)

5

A) (4, -1)

Translate 3 right, 5 down: (1+3, 4-5) = (4, -1)

6

A) The figures are congruent because both transformations are rigid

Reflection and translation are both rigid transformations that preserve size and shape.

FAST Quiz Scoring Guide

Score	Interpretation	Recommended Action
6/6	Mastery	Ready for complex sequences and composition of transformations.
4-5/6	Approaching Mastery	Review specific transformation rules or congruence/similarity concepts.
2-3/6	Developing	Reteach with visual models. Practice one transformation type at a time.
0-1/6	Needs Intervention	Small group instruction. Use manipulatives and tracing paper.