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A free printable worksheet that pairs with the Let's Get to the Point game. The worksheet prints first, and the answer key prints on its own page after it, so you can leave it off. To make a PDF, click Print and choose "Save as PDF."

Transformations on the Coordinate Plane

Grade 8 · CCSS 8.G.A.1 · Pairs with the Let's Get to the Point game
Name
Date
Translation: add to the coordinates, (x, y) → (x + h, y + k).   Reflection over the x-axis: (x, y) → (x, −y); over the y-axis: (x, y) → (−x, y).
Rotation about the origin: 90° counterclockwise (x, y) → (−y, x); 180° (x, y) → (−x, −y); 90° clockwise (x, y) → (y, −x).

Part A: Translations

1. Move (2, −1) by the rule (x − 4, y + 3).
Image: ( )
2. Move (−3, 5) 6 units right and 2 units down.
Image: ( )
3. Move (0, −4) by the rule (x + 5, y + 6).
Image: ( )
4. What rule moves (1, 1) to (−3, 4)?
(x , y )

Part B: Reflections

5. Reflect (5, 3) over the x-axis.
Image: ( )
6. Reflect (−2, 4) over the y-axis.
Image: ( )
7. Reflect (−6, −1) over the x-axis.
Image: ( )
8. Reflect (3, −7) over the y-axis.
Image: ( )

Part C: Rotations about the origin

9. Rotate (4, 1) 90° counterclockwise.
Image: ( )
10. Rotate (2, 5) 180°.
Image: ( )
11. Rotate (−3, 2) 90° clockwise.
Image: ( )
12. Rotate (6, −1) 270° counterclockwise.
Image: ( )

Part D: Put it on the grid

13. Plot A(−3, 2). Reflect it over the y-axis and label the image A′. Then rotate A′ 180° about the origin and label that image A″.
A′ ( )   A″ ( )
14. Find the mistake. Alex reflected (4, −2) over the x-axis and got (−4, −2). What did Alex do wrong? What's the correct image?
Correct: ( )

15. After any translation, reflection or rotation, is the new figure congruent to the original? Explain.

Play the game: studentmathgames.com/lets-get-to-the-point© 2026 Mr. H · Free for classroom use

Answer Key: Transformations

For the teacher
  1. (2 − 4, −1 + 3) → (−2, 2)
  2. (−3 + 6, 5 − 2) → (3, 3)
  3. (0 + 5, −4 + 6) → (5, 2)
  4. x changes by −4, y by +3 → (x − 4, y + 3)
  5. (5, −3)
  6. (2, 4)
  7. (−6, 1)
  8. (−3, −7)
  9. (−y, x) → (−1, 4)
  10. (−x, −y) → (−2, −5)
  11. (y, −x) → (2, 3)
  12. 270° counterclockwise is the same as 90° clockwise: (y, −x) → (−1, −6)
  13. A′ = (3, 2); A″ = (−3, −2)
  14. Alex changed the sign of x, which is a reflection over the y-axis. Over the x-axis only y changes: (4, 2)
  15. Yes. Translations, reflections and rotations are rigid motions: they keep every length and angle, so the image is congruent.

The game names these same mistakes after a miss: wrong direction, wrong axis, swapped coordinates, and moving only one coordinate. Real tracing paper makes #9–12 much easier for students who are stuck.

Full Teacher Guide: studentmathgames.com/lets-get-to-the-point/guide.html© 2026 Mr. H