Symmetry and Transformations summary

Key learning points

• Line symmetry: mirror lines that map the shape to itself.
• Order of rotational symmetry: how many times it fits in a $360^\circ$ turn.
• Regular polygons have equal numbers of lines of symmetry and rotational order.

Worked example 1 — Reflection

Reflect $(2,3)$ in the $y$-axis.

Working

Negate $x$.

Worked example 2 — Rotation

Rotate $(1,0)$ by $90^\circ$ anticlockwise about O.

Working

$(x,y)\to(-y,x)$.

Worked example 3 — Rotational order

Order of rotational symmetry of a regular pentagon?

Working

Every $72^\circ$.

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.