Carry out and describe the four transformations - translation, reflection, rotation and enlargement (including negative and fractional scale factors at Higher tier) - and identify the result of combined transformations.

What this dot point is asking

WJEC asks you to carry out and to describe the four transformations: translation, reflection, rotation and enlargement, including negative and fractional scale factors at Higher tier, and to identify the result of combining two transformations. The recurring exam command is "describe fully the single transformation", which demands every detail needed to specify it uniquely. The marks reward both performing a transformation accurately on a grid and giving a complete, correctly worded description, so knowing exactly what each type requires is the key skill.

Translation

A translation slides every point the same distance and direction.

So translating by $\binom{4}{-3}$ moves every point $4$ right and $3$ down. To describe a translation fully, give the column vector. Translations connect directly to the vectors topic.

Reflection

A reflection flips a shape across a mirror line.

Each point moves to the opposite side of the mirror line, the same perpendicular distance away. Common mirror lines are the $x$-axis ($y = 0$), the $y$-axis ($x = 0$), and the diagonals $y = x$ and $y = -x$. To describe a reflection fully, name the mirror line by its equation. Reflecting in $y = x$ swaps the coordinates: $(a, b) \to (b, a)$.

Rotation

A rotation turns a shape about a fixed point.

Tracing paper helps: mark the centre, trace the shape, hold the centre with a pencil and turn. To describe a rotation fully, give the angle, the direction and the centre.

Enlargement

An enlargement changes a shape's size from a centre.

To describe an enlargement fully, give the scale factor and the centre. To find the centre, draw straight lines through corresponding points of the object and image; they meet at the centre.

Combining transformations

Two transformations applied in turn can often be replaced by one.

Why this matters

Transformations are a reliable source of marks across both components, tested as accurate constructions on a grid and as full descriptions. The "describe fully" command is where candidates most often drop marks, by naming the type but omitting a detail (the mirror line, the centre, the scale factor) or by giving two transformations when one is asked for. At Higher tier, negative and fractional scale factors and combined transformations add depth, and the topic links to vectors (for translations) and to similarity (enlargement preserves shape but not size).