GCSE MATHS • HIGHER TIER

Rotation Made Simple

Rotate points and shapes accurately using the correct centre, angle and direction.

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Clear method

Exam practice

Worked proofs

Rotation in Four Moves

1

Find the Centre

Identify the fixed point around which the shape rotates.

2

Choose the Angle

Identify the required rotation angle such as 90°, 180° or 270°.

3

Check the Direction

Decide whether the turn is clockwise or anti-clockwise.

4

Rotate and Plot

Rotate each vertex, plot the new points and join them to form the image.

What You’ll Learn

Understand what a rotation is.

Recognise common GCSE rotation angles.

Distinguish clockwise from anti-clockwise.

Understand the centre of rotation.

Rotate coordinates about the origin.

Perform rotations of shapes on coordinate grids.

Describe rotations fully.

Key Rules

Centre of rotation

A rotation turns a shape around a fixed centre of rotation.

Angle & direction

Always identify the angle and whether the turn is clockwise or anti-clockwise.

90° clockwise

(x, y) → (y, −x)

90° anti-clockwise

(x, y) → (−y, x)

180° rotation

(x, y) → (−x, −y)

Worked Proof: Rotation

Step-by-Step Method

  • 1. Identify the centre of rotation.
  • 2. Identify the angle of rotation.
  • 3. Check whether the rotation is clockwise or anti-clockwise.
  • 4. Rotate each vertex around the centre.
  • 5. Plot the new vertices accurately.
  • 6. Join the points to complete the rotated shape.

More Worked Examples

1

Rotate a point 90° clockwise about the origin.

Point: (2, 4)

Rule: (x, y) → (y, -x)
(2, 4) → (4, -2)
Answer: (4, -2)

2

Rotate a point 90° anti-clockwise about the origin.

Point: (3, 1)

Rule: (x, y) → (-y, x)
(3, 1) → (-1, 3)
Answer: (-1, 3)

3

Rotate a point 180° about the origin.

Point: (5, 2)

Rule: (x, y) → (-x, -y)
(5, 2) → (-5, -2)
Answer: (-5, -2)

4

A triangle is rotated 90° clockwise around the origin.

Vertex A = (1, 2)

(1, 2) → (2, -1)
Answer: New vertex A is (2, -1).
  • Common GCSE Mistakes
  • Confusing clockwise and anti-clockwise.
  • Using the wrong centre of rotation.
  • Rotating by the wrong angle.
  • Forgetting that the shape stays the same size.
  • Misplotting rotated coordinates.
  • Exam Tips
  • Misplotting rotated coordinates.
  • Check the angle carefully.
  • Confirm clockwise or anti-clockwise direction.
  • Keep every vertex the same distance from the centre.
  • Learn the common coordinate rules about the origin.
  • When describing a rotation, include angle, direction and centre.

Skills Used in Rotation

Transformations

Coordinates

Centre of Rotation

Angles

Spatial Awareness

Accurate Plotting

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Printable Worksheet

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Interactive Quiz

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Exam-Style Questions

Timed questions to build confidence for the real exam.

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Watch the Rotation Tutorial

Step-by-step walkthroughs of Rotation with clear methods and exam tips.

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Frequently Asked Questions

A rotation turns a shape around a fixed point called the centre of rotation.

No. A rotation keeps the same size and shape but changes orientation.

The angle, direction and centre of rotation.

(x, y) → (y, -x).

(x, y) → (-y, x).

It is equivalent to 90° anti-clockwise.