8th Grade Math · Transformations
Rotations Worksheets
Free and printable, with a full answer key. Every worksheet is generated fresh, so you can hand a different version to every student.
Turn a figure 90°, 180° or 270° about the origin, clockwise and counterclockwise.
Or start with a ready-made version:
How it works: a quick refresher
For the adult at the table. These are the rules the worksheet practices, followed by one problem worked from start to finish.
| To do this | Use this rule |
|---|---|
| Translate a units right and b units up | (x, y) → (x + a, y + b) |
| Reflect over the x-axis | (x, y) → (x, −y) |
| Reflect over the y-axis | (x, y) → (−x, y) |
| Reflect over the line y = x | (x, y) → (y, x) |
| Reflect over the line y = −x | (x, y) → (−y, −x) |
| Rotate 90° counterclockwise about the origin | (x, y) → (−y, x) |
| Rotate 90° clockwise about the origin | (x, y) → (y, −x) |
| Rotate 180° about the origin | (x, y) → (−x, −y) |
Worked example
Rotate triangle A(1, 2), B(4, 2), C(4, 5) 90° counterclockwise about the origin.
- Apply the rule (x, y) → (−y, x) to each vertex.
- A(1, 2) becomes A′(−2, 1).
- B(4, 2) becomes B′(−2, 4).
- C(4, 5) becomes C′(−5, 4).
- Plot the three new points and connect them. The triangle keeps its size and shape; only its position changes.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- Rotations Worksheets, version 1Worksheet PDFAnswer key PDF
- Rotations Worksheets, version 2Worksheet PDFAnswer key PDF
- Rotations Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 8th grade math (geometry) and aligned to CCSS 8.G.A.3. It also works as review in later grades.
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet ID printed at the bottom of each page pairs a sheet with its key.
- Do these worksheets include dilations?
- Not yet. They cover the three rigid transformations: translations, reflections and rotations. Every image is the same size and shape as the original.
- Are rotations always about the origin?
- Yes. Every rotation is 90°, 180° or 270° about the origin (0, 0).
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.