The four transformations

A transformation maps an object to an image. CCEA expects you to describe fully and perform each.

Translation

Shifts every point by the same vector $\binom{a}{b}$, where a is the horizontal shift and b is the vertical shift.

To describe: state the vector, e.g. "Translation by vector (3, −2)". No invariant points unless the vector is zero.

Reflection

Flips the shape across a mirror line. Each image point is the same perpendicular distance from the mirror as the object.

To describe fully: state "reflection in the line y = …" or "reflection in the x-axis". Common mirror lines: x-axis (y = 0), y-axis (x = 0), y = x, y = −x.

Rotation

Turns the shape by an angle about a centre.

To describe fully: state "rotation, 90° clockwise (or anticlockwise), about (a, b)". Common rotations: 90°, 180°, 270°. (180° rotation = "half turn" — direction is irrelevant.)

Tip: trace the original onto tracing paper, hold it at the centre, and turn.

Enlargement

Scales every point by a scale factor k from a centre of enlargement.

To describe fully: state "enlargement, scale factor k, centre (a, b)".

• k > 1 → larger.
• 0 < k < 1 → smaller.
• k < 0 → image on opposite side of centre, inverted.
• k = −1 → equivalent to a 180° rotation about the centre.

Combining transformations

Composite transformations are described in the order applied. The final result may equal a single transformation — e.g. two reflections in parallel mirrors = a translation; two reflections in intersecting mirrors = a rotation.

Common CCEA exam tip

When describing, list every required piece of information. CCEA mark schemes use bullet points: e.g. for rotation, you need (1) "rotation", (2) angle, (3) direction (unless 180°), (4) centre. Missing any one = lose 1 of 3 marks.