In the previous section, you have seen a translation which moves a given object along a given direction while preserving size and shape of the object. Another rigid motion is a reflection.

A reflection fixes a mirror line in the plane and flips each point from one side of the mirror line to the point on the other side at the same distance from the line. For instance, the following figure shows the reflection of point P to P′ and ∆ABC to ∆A′B′C′ using a horizontal and vertical mirror lines.

Every reflection has a mirror line, also called line of reflection. It is helpful to think of the mirror line as an actual mirror and the image of the object as its image in the mirror. The formal definition of reflection is as follows.

Definition

Reflection

Let L be a fixed line in the plane. A reflection M about the line L is a transformation of the plane onto itself which carries each point P of the plane into the point P′ of the plane such that L is the perpendicular bisector of PP′.