## Reflection

 When a shape or point is reflected its image is on the opposite side of a mirror line or axis of symmetry. The mirror line is halfway between the shape and its image The axis of symmetry, often a dotted line, is usually shown by the letter m.

### Properties of Reflection

When a shape is reflected, points on the image are indicated with a dash, e.g. P´

Triangle PQR maps to triangle P´Q´R´

• The object is the same distance in front of the mirror line m as the image is behind it. i.e. PT = P´ T
• Length, angle size and area do not change. (They are said to be invariant.)
i.e.  Length PQ = Length P´Q´ PQR =  P´Q´R´ Area PQR = Area P´Q´R´
• Any point on the mirror line does not move. i.e. It is invariant.

i.e. S  S'

To see examples of reflections −

### Location of Mirror Line

 To find the mirror line given a line and its image: 1. Join the point and its image with a line. 2. Draw the perpendicular bisector of this line.i.e. Halfway, and at right angles. lineimage of line