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Transformations worksheet

Grade 8 math, Common Core 8.G.A.3. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Transformations

Grade 8 math, Common Core 8.G.A.3

Find the coordinates of each image point.

  1. 1.
    Triangle ABC has A(3, −8), B(6, −8) and C(3, −3). It is translated 1 right and 3 up. Find A′, B′ and C′.
  2. 2.
    Rotate (1, 8) 180° about the origin.
  3. 3.
    Dilate (5, −2) by a scale factor of 2 about the origin.
  4. 4.
    Translate (2, 5) 5 units left and 6 units down.
  5. 5.
    Triangle ABC has A(3, 7), B(6, 7) and C(3, 10). It is translated 2 left and 5 up. Find A′, B′ and C′.
  6. 6.
    Dilate (−4, −16) by a scale factor of 12 about the origin.
  7. 7.
    Triangle ABC has A(3, 1), B(6, 1) and C(3, 4). It is translated 4 left and 5 down. Find A′, B′ and C′.
  8. 8.
    Translate (−3, −2) 2 units left and 2 units down.
  9. 9.
    Reflect (−2, 7) over the x-axis.
  10. 10.
    Translate (3, −8) 4 units left and 4 units up.
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Transformations

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. A′(4, −5), B′(7, −5), C′(4, 0)

  2. 2. (−1, −8)

    (x, y) → (−x, −y)

  3. 3. (10, −4)

    Multiply both coordinates by 2

  4. 4. (−3, −1)

    (2 − 5, 5 − 6)

  5. 5. A′(1, 12), B′(4, 12), C′(1, 15)

  6. 6. (−2, −8)

    Multiply both coordinates by 12

  7. 7. A′(−1, −4), B′(2, −4), C′(−1, −1)

  8. 8. (−5, −4)

    (−3 − 2, −2 − 2)

  9. 9. (−2, −7)

  10. 10. (−1, −4)

    (3 − 4, −8 + 4)

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About transformations

A transformation moves a shape on the coordinate plane. A translation slides it, a reflection flips it over a line, a rotation turns it around a point, and a dilation stretches or shrinks it. Rules: reflect over the x-axis (x, y) → (x, −y); over the y-axis (x, y) → (−x, y); rotate 90° clockwise (x, y) → (y, −x); 180° (x, y) → (−x, −y); dilate by k (x, y) → (kx, ky).

Worked example 1

Rotate (4, −4) 90° counterclockwise about the origin.
  1. Step 1.(x, y) → (−y, x)

Answer: (4, 4)

Worked example 2

Translate (−1, −4) 1 unit left and 4 units down.
  1. Step 1.(−1 − 1, −4 − 4)

Answer: (−2, −8)

Worked example 3

Rotate (−8, 2) 90° clockwise about the origin.
  1. Step 1.(x, y) → (y, −x)

Answer: (2, 8)

Watch out for

  • Left and down mean subtract; right and up mean add.
  • Rotating 90° clockwise and counterclockwise give different points. Check the direction.
  • Translations, reflections and rotations keep the size and shape. Dilations change the size.

Practice transformations online

On StudyWiz, your kid can practice transformations with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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