GEOMETRY

Rotations

Learn the reliable method for rotations, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A rotation turns a shape through a stated angle about a fixed centre.

Picture itTrack the angle turn
2 · THE METHOD

Follow these steps

  1. Mark the centre of rotation.
  2. Track direction and turn size.
  3. Check that every vertex remains the same distance from the centre.
3 · WORKED EXAMPLES

See the method in action

Example 1

Point P is rotated 90° anticlockwise about the origin. What are the coordinates of its image?

P(3, 1)xyO
  1. A 90° anticlockwise rotation maps (x, y) to (−y, x).
  2. Therefore (3, 1) maps to (-1, 3).
Answer: (-1, 3)
Example 2

Which transformation maps the image triangle back onto the original triangle?

originalimageO
  1. To reverse a rotation, keep the centre and angle but reverse its direction.
  2. The inverse is 90° clockwise about O.
Answer: A rotation of 90° clockwise about O
4 · ELEVENSPRINT TIP

A useful shortcut

Check that every vertex remains the same distance from the centre.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.