# Centre Of Rotation Gcse Maths Coursework

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

Rotation is an example of a **transformation**. A transformation is a way of changing the size or position of a shape.

The shape has been rotated 90° (a quarter turn) clockwise about the centre of rotation

The shape has been rotated 180° (a half-turn) about the centre of rotation

The shape has been rotated 90° (a quarter turn) anticlockwise about the centre of rotation

The triangle PQR has been rotated 90° anticlockwise about the origin O to create the image P'Q'R'.

### Example

Rotate the triangle PQR 90° anticlockwise about the origin.

Tracing paper can be used to rotate a shape.

Trace the shape and the centre of rotation.

Hold down the tracing paper with a pencil on the centre of rotation.

Rotate the tracing paper and copy the image.

- QQuestion
Describe the transformation of the rectangle ABCD.

- A
Each corner of the image A'B'C'D' is the same distance from the origin as the original shape. The origin is the centre of rotation.

The rectangle ABCD has been rotated 180° about the origin (the direction is not required because it is a half turn).

- the centre of rotation
- the angle of rotation
- the direction of rotation

## Rotations about any point

Remember that a point and its image are always the same distance from the centre of rotation.

**Example**

Describe the rotation which moves **ABCD** to **A'B'C'D'** in this diagram.

The **centre of rotation** is **(0, -1)**.

We can see that **A** is the same distance from (0, -1) as **A'**.

**D** is the same distance from (0, -1) as **D'**.

The **angle of rotation** is **90° clockwise**.

It is possible to use constructions to find the centre of rotation, but this can be time-consuming and complicated. Try to find the centre by observation, but remember that each point and its image **must** be the same distance from the centre of rotation.

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