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

The Eduqas geometry content asks you to describe and perform the four transformations: translation, rotation, reflection and enlargement, including negative and fractional scale factors at Higher tier, and to recognise the result of combining two of them. Transformations test both precise drawing and precise description, and Eduqas's "describe fully the single transformation" instruction demands the exact details that define each one. It appears at both tiers, with enlargement (especially negative and fractional factors) reaching into Higher.

Translation

A translation slides every point of a shape the same distance in the same direction, with no turning or resizing.

So a translation by $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$ moves the shape $3$ right and $2$ down. A full description needs only the word "translation" and the vector; the sign convention is the usual source of error, so check that down and left are negative.

Rotation

A rotation turns a shape about a fixed point.

A $180^\circ$ rotation is the same clockwise or anticlockwise, so the direction can be omitted only in that case. Tracing paper is the practical tool: place it over the shape, pin the centre, and turn. To describe a rotation fully, state all three details.

Reflection and enlargement

A reflection flips a shape across a mirror line, and an enlargement resizes it from a centre.

For an enlargement, each point moves so that its distance from the centre multiplies by the scale factor. A scale factor of $3$ triples every distance from the centre; a fractional factor such as $\tfrac{1}{2}$ halves them (a reduction). At Higher tier, a negative scale factor enlarges and places the image on the opposite side of the centre, effectively rotating it $180^\circ$ as well.

Combining transformations and describing fully

A combination of two transformations can sometimes be described as a single one, which Eduqas tests with "describe the single transformation equivalent to..." questions. The crucial exam skill is the full description: a translation needs its vector, a rotation needs angle, direction and centre, a reflection needs its mirror-line equation, and an enlargement needs its scale factor and centre. Giving only the type of transformation, without these details, loses marks even when the type is correct.