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).

Three pieces of information are needed to rotate a shape:
  • 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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