Describe and perform the four transformations (translation, rotation, reflection and enlargement, including negative and fractional scale factors at Higher tier) and combine them.

What this dot point is asking

OCR references G7 and G8 cover the four transformations: translation, rotation, reflection and enlargement, including negative and fractional scale factors at Higher tier. You must both perform a transformation on a grid and describe a given one fully. Transformations test precise communication, because each type needs specific information to describe it, and OCR penalises an incomplete description. The topic appears on every tier.

Translations

A translation moves every point the same distance and direction.

So a translation by $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$ moves every vertex $3$ right and $2$ down. To describe a translation, give the single column vector; describing it in words ("moved right and down") is not enough for full marks. Translations link directly to the vectors topic.

Rotations and reflections

These two transformations change orientation.

For a rotation, tracing the movement of one vertex around the centre, often using tracing paper, gives the image; a $180^\circ$ rotation needs no direction because clockwise and anticlockwise coincide. For a reflection, each point moves to the same perpendicular distance on the other side of the mirror line, so points on the line stay fixed. Naming the mirror line precisely is essential.

Enlargements

An enlargement changes size from a fixed centre.

So an enlargement of scale factor $3$ from a centre triples every distance from that centre, and a scale factor of $\tfrac{1}{2}$ halves them. A negative scale factor of $-2$ doubles the distances but on the opposite side of the centre, turning the image upside down. The lengths scale by the factor, the area by the factor squared.

Why transformations matter

Transformations describe symmetry and movement, and OCR's marks hinge on the completeness of the description: a rotation without a centre, or a reflection without a named line, scores partial marks at best. Knowing that an enlargement changes area by the square of the scale factor links transformations to ratio and to similar shapes. Combining two transformations into a single equivalent one is a Higher-tier extension that rewards careful tracking of each step.