Transformations summary

Key learning points

• Translation → column vector; reflection → mirror line; rotation → centre, angle, direction; enlargement → centre and scale factor.
• Scale factor $>1$ enlarges; $0<k<1$ reduces; negative $k$ rotates $180^\circ$ as well.
• Invariant points stay fixed (e.g. points on a mirror line).

Worked example 1 — Translation

Translate $(1,2)$ by $\begin{pmatrix}3\\-1\end{pmatrix}$.

Working

Add components.

Worked example 2 — Enlargement

Centre O, SF $2$, point $(3,1)$. Image?

Working

Multiply coordinates by SF.

Worked example 3 — Reflection

Reflect $(4,-2)$ in the $x$-axis.

Working

Negate $y$.

Worked example 4 — Enlargement scale factor

Image lengths are 3 times object lengths from centre O. Scale factor?

Working

Also state the centre of enlargement in a full description.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.