Worksheets · Geometry

Transformations worksheet

Each transformation is one rule about what happens to the coordinates. Learn the six rules and the whole topic is arithmetic.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Transformations

Date Period

Find the image of each point.

  1. Rotate 90∘ counterclockwise about the origin-10-10-5-55510100ABC
  2. Translate (−14,−7) by (x−4,  y−7)
  3. Reflect over the x-axis-10-10-5-55510100ABC
  4. Translate (5,−10) by (x+3,  y+7)
  5. Rotate 180∘ about the origin-10-10-5-55510100ABC
  6. Translate (−11,2) by (x−9,  y+4)
  7. Rotate 270∘ counterclockwise about the origin-10-10-5-55510100ABC
  8. Translate (12,2) by (x+5,  y+8)
  9. Rotate 270∘ counterclockwise about the origin-10-10-5-55510100ABC
  10. Translate (−2,−5) by (x+8,  y−12)
  11. Rotate 270∘ counterclockwise about the origin-10-10-5-55510100ABC
  12. Translate (5,−2) by (x−10,  y+2)
  13. Rotate 90∘ counterclockwise about the origin-10-10-5-55510100ABC
  14. Translate (−3,−14) by (x+13,  y−4)
  15. Rotate 270∘ counterclockwise about the origin-10-10-5-55510100ABC
  16. Translate (−13,−13) by (x+10,  y−6)
  17. Reflect over the y-axis-10-10-5-55510100ABC
  18. Translate (−11,−4) by (x+5,  y+8)
  19. Reflect over the line y = x-10-10-5-55510100ABC
  20. Translate (−9,1) by (x−13,  y+6)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

TransformationsAnswer keyVersion 1

Date Period

Find the image of each point.

  1. Rotate 90∘ counterclockwise about the origin-10-10-5-55510100ABCA'B'C'(−4,−4),  (−4,−7),  (−8,−7)
  2. Translate (−14,−7) by (x−4,  y−7)(−18,−14)
  3. Reflect over the x-axis-10-10-5-55510100ABCA'B'C'(3,−3),  (7,−3),  (4,−8)
  4. Translate (5,−10) by (x+3,  y+7)(8,−3)
  5. Rotate 180∘ about the origin-10-10-5-55510100ABCA'B'C'(−2,−2),  (−8,−2),  (−7,−5)
  6. Translate (−11,2) by (x−9,  y+4)(−20,6)
  7. Rotate 270∘ counterclockwise about the origin-10-10-5-55510100ABCA'B'C'(−4,4),  (−4,9),  (−8,5)
  8. Translate (12,2) by (x+5,  y+8)(17,10)
  9. Rotate 270∘ counterclockwise about the origin-10-10-5-55510100ABCA'B'C'(1,4),  (1,9),  (4,8)
  10. Translate (−2,−5) by (x+8,  y−12)(6,−17)
  11. Rotate 270∘ counterclockwise about the origin-10-10-5-55510100ABCA'B'C'(4,1),  (4,5),  (7,2)
  12. Translate (5,−2) by (x−10,  y+2)(−5,0)
  13. Rotate 90∘ counterclockwise about the origin-10-10-5-55510100ABCA'B'C'(6,4),  (6,9),  (9,8)
  14. Translate (−3,−14) by (x+13,  y−4)(10,−18)
  15. Rotate 270∘ counterclockwise about the origin-10-10-5-55510100ABCA'B'C'(3,−2),  (3,−8),  (8,−3)
  16. Translate (−13,−13) by (x+10,  y−6)(−3,−19)
  17. Reflect over the y-axis-10-10-5-55510100ABCA'B'C'(2,1),  (5,1),  (5,4)
  18. Translate (−11,−4) by (x+5,  y+8)(−6,4)
  19. Reflect over the line y = x-10-10-5-55510100ABCA'B'C'(−1,−4),  (−1,−9),  (−5,−5)
  20. Translate (−9,1) by (x−13,  y+6)(−22,7)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Rotate (3,−2) 90∘ counterclockwise about the origin

  1. A quarter turn counterclockwise sends (x, y) to (-y, x).
  2. So the -2 becomes 2 and moves to the front.

The answer is (2,3).

Where students go wrong

Turning the wrong way, or swapping without changing a sign. A quick check: sketch the point roughly and see which quadrant it should land in. If the answer is in the wrong quarter of the plane, the rule was misremembered.

Also called translations, reflections, rotations or coordinate transformations.

What you can put on this worksheet

On a grid, with the image drawn
Reflect over the y-axis → (−2,−5),  (−6,−5),  (−2,−9)
Translations
Translate (3,1) by (x+2,  y+2) → (5,3)
Reflections
Reflect (3,1) over the y-axis → (−3,1)
Rotations
Rotate (3,1) 180∘ about the origin → (−3,−1)

Questions about these worksheets

Yes. Every transformations sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the transformations questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: on a grid, with the image drawn, translations, reflections and rotations. Tick as many as you want and set how many of each, or let it spread them evenly.

Turning the wrong way, or swapping without changing a sign. A quick check: sketch the point roughly and see which quadrant it should land in. If the answer is in the wrong quarter of the plane, the rule was misremembered.