Transformations

3) Rotation

Rotation turns a shape around a fixed point called the centre of rotation. Three pieces of information are needed to rotate a shape:

1) the centre of rotation
2) the angle of rotation
3) the direction of rotation

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

Triangle (PQR) with dashed line from P to the origin and another dashed line from origin to P', where triangle (P'Q'R') sits
Question 1

Rotate the triangle PQR 90° anticlockwise about the origin.

Triangle (PQR) with dashed line from P to the origin

Tracing paper can be used to rotate a shape.

Answer: 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.

Tracing paper overlaid and triangle (P'Q'R') drawn in

Question 2

Describe the transformation of the rectangle ABCD.

Rectangle (ABCD) rotated 180degrees to produce rectangle (A'B'C'D')

Answer: 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).


Different centres of rotation

The centre of rotation may not be at the origin.

Rotate the rectangle ABCD 90° clockwise about the point (0,-1).

Graph showing rectangle ABCD rotated about point (0,-1)

Each corner of the image A’B’C’D’ is the same distance from the centre of rotation as the original shape.

Rectangle (ABCD) rotated to give rectangle (A'B'C'D')

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