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.)
        Length PQ = Length P´Q´
    y8_Reflection_04.gifPQR = y8_Reflection_04.gif P´Q´R´
    Area y8_Reflection_05.gifPQR = Area y8_Reflection_05.gifP´Q´R´
  • Any point on the mirror line does not move. i.e. It is invariant.

    i.e. S y8_Reflection_06.gif S'

To see examples of reflections − y8_Reflection_07.gif



Location of Mirror Lineswans.jpg


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.

liney8_Reflection_08.gifimage of line