GCSE Maths: Transformations of Shapes Guide

Translation

A translation moves a shape without rotating or resizing it, described by a vector such as (3, -2), meaning 3 right and 2 down.

Reflection

A reflection flips a shape over a mirror line, such as the x-axis, y-axis, or a line like y = x. Every point ends up the same distance from the mirror line as its original point, on the opposite side.

Rotation

A rotation turns a shape around a fixed centre point by a given angle and direction (clockwise or anticlockwise). Tracing paper can help check rotations accurately.

Enlargement

An enlargement resizes a shape from a centre of enlargement by a scale factor. A scale factor greater than 1 makes the shape bigger; between 0 and 1 makes it smaller; a negative scale factor also flips it through the centre.

Common mistakes

• Forgetting to state the direction of a rotation (clockwise or anticlockwise).
• Describing a translation without a vector, or getting the vector's signs the wrong way round.
• Measuring enlargement distances from the wrong point instead of the centre of enlargement.