In a reflection, the mirror line perpendicularly bisects each segment joining a point to its image. Points on the mirror line stay fixed. Measure the shortest distance to the line, then place the image the same distance on the other side. Example Reflection in x=2 sends (5,1) to (-1,1), since both are three units from the line. **Mirror line** | **Coordinate rule** x-axis | (x,y) to (x,-y) y-axis | (x,y) to (-x,y) y=x | (x,y) to (y,x) y=-x | (x,y) to (-y,-x) A complete reflection description names the mirror line, such as y=-x. Reversing the order of vertices helps distinguish a reflection from a rotation.

In a reflection, the mirror line perpendicularly bisects each segment joining a point to its image. Points on the mirror line stay fixed. Measure the shortest distance to the line, then place the image the same distance on the other side.

Reflection in \(x=2\) sends \((5,1)\) to \((-1,1)\), since both are three units from the line.

A complete reflection description names the mirror line, such as \(y=-x\). Reversing the order of vertices helps distinguish a reflection from a rotation.

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.

Mirror line	Coordinate rule
x-axis	\((x,y)\mapsto(x,-y)\)
y-axis	\((x,y)\mapsto(-x,y)\)
\(y=x\)	\((x,y)\mapsto(y,x)\)
\(y=-x\)	\((x,y)\mapsto(-y,-x)\)

Reflection in a line

Reflection in a line