Practice: Transformations

Part A: Translations

Directions: Find the coordinates of each point after the given translation.

1. A(4, 2) translated 3 left, 5 up

A' = (_______, _______)

2. B(-1, 6) translated 4 right, 2 down

B' = (_______, _______)

3. C(0, -3) translated 5 left, 3 down

C' = (_______, _______)

4. D(-5, -4) translated 7 right, 1 up

D' = (_______, _______)

Part B: Reflections

Directions: Find the coordinates after reflecting over the given axis.

5. E(3, -5) reflected over x-axis

E' = (_______, _______)

6. F(-4, 2) reflected over y-axis

F' = (_______, _______)

7. G(6, -1) reflected over y-axis

G' = (_______, _______)

8. H(-2, -7) reflected over x-axis

H' = (_______, _______)

Part C: Rotations about the Origin

Directions: Find the coordinates after the given rotation about the origin.

9. I(2, 5) rotated 90° CCW

(x, y) → (-y, x)

I' = (_______, _______)

10. J(-3, 4) rotated 180°

(x, y) → (-x, -y)

J' = (_______, _______)

11. K(1, -6) rotated 90° CW

(x, y) → (y, -x)

K' = (_______, _______)

12. L(-4, -2) rotated 270° CCW

(same as 90° CW)

L' = (_______, _______)

Part D: Dilations (center at origin)

Directions: Find the coordinates after dilation with the given scale factor.

13. M(4, -2) with scale factor 3

M' = (_______, _______)

14. N(-6, 8) with scale factor 1/2

N' = (_______, _______)

Part E: Identify the Transformation

Directions: Identify the transformation that maps the preimage to the image.

#	Preimage	Image	Transformation
15.	(3, 4)	(3, -4)	_______________________
16.	(2, 5)	(-5, 2)	_______________________
17.	(-1, 3)	(-4, 7)	_______________________
18.	(4, 2)	(12, 6)	_______________________

Part F: Sequences of Transformations

Directions: Apply the transformations in order. Show your work.

19. Start with P(2, 3). First reflect over the x-axis, then translate 4 units left.

After reflection: P' = (_______, _______)

After translation: P'' = (_______, _______)

20. Start with Q(-1, 4). First rotate 90° CCW about the origin, then reflect over the y-axis.

After rotation: Q' = (_______, _______)

After reflection: Q'' = (_______, _______)

21. A figure is translated, then reflected over the x-axis. Is the image congruent or similar to the original? Explain.

22. A figure is dilated by a scale factor of 2, then translated 5 units right. Is the image congruent or similar to the original? Explain.

Challenge: Think About It!

23. Point R(a, b) is reflected over the x-axis, then reflected over the y-axis. What single transformation would give the same result?

24. A square with vertices at (1, 1), (3, 1), (3, 3), and (1, 3) is dilated by a scale factor of 2. By what factor does the AREA change?