A rotation needs three facts: the centre, the angle and the direction (clockwise or anticlockwise). A half turn, 180°, needs no direction. About the origin the rules are:

90° clockwise: (x, y) → (y, −x)
90° anticlockwise: (x, y) → (−y, x)
180°: (x, y) → (−x, −y)

About any other centre C, work with the vector from C to the point, turn that vector, and add it back on to C.

1. Rotate P(5, 3) 90° clockwise about C(2, 1)
2. From C to P: 3 across, 2 up
3. Turned 90° clockwise: (3, 2) → (2, −3)
4. P′ = (2 + 2, 1 − 3) = (4, −2)

On a paper, tracing paper is allowed. Trace the shape, hold the centre still with your pencil and turn the paper.

An enlargement with scale factor k and centre C sends every point to k times as far from C, in the same direction. Every length is multiplied by k. A scale factor between 0 and 1, such as 1/2, makes the shape smaller: it is still called an enlargement.

To find the centre of an enlargement, draw straight lines through matching vertices of the shape and its image and extend them: they meet at the centre. The scale factor is a length on the image divided by the matching length on the original.

• Turning the wrong way. Clockwise is the way the hands of a clock move.
• Enlarging from the origin when the centre is somewhere else. Always measure from the given centre.
• Writing "Rotation 90° about (2, 1)" with no direction, or "Enlargement, scale factor 3" with no centre. Each loses a mark.