A rotation keeps every point the same distance from a fixed centre and turns every joining ray through the same angle. State the centre, angle and direction. For 180, either direction gives the same result. **About the origin** | **Coordinate rule** 90 anticlockwise | (x,y) to (-y,x) 90 clockwise | (x,y) to (y,-x) 180 | (x,y) to (-x,-y) For another centre, first measure coordinates relative to it. About (1,1), point (3,2) has displacement (2,1). A 90 anticlockwise turn changes this to (-1,2), so the image is (0,3). Do not apply an origin rule directly when the centre is elsewhere. A 270 clockwise turn equals a 90 anticlockwise turn.

A rotation keeps every point the same distance from a fixed centre and turns every joining ray through the same angle. State the centre, angle and direction. For \(180^\circ\), either direction gives the same result.

For another centre, first measure coordinates relative to it. About \((1,1)\), point \((3,2)\) has displacement \((2,1)\). A \(90^\circ\) anticlockwise turn changes this to \((-1,2)\), so the image is \((0,3)\).

Do not apply an origin rule directly when the centre is elsewhere. A \(270^\circ\) clockwise turn equals a \(90^\circ\) anticlockwise turn.

Plane Transformations

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

About the origin	Coordinate rule
\(90^\circ\) anticlockwise	\((x,y)\mapsto(-y,x)\)
\(90^\circ\) clockwise	\((x,y)\mapsto(y,-x)\)
\(180^\circ\)	\((x,y)\mapsto(-x,-y)\)

Rotation about a centre

Rotation about a centre