Rotations of Figures in a Plane
Concept

Reflection of Geometric Objects

A reflection is a transformation in which every point of a figure is reflected across a line. The line across the points are reflected in what is called the line of reflection. This acts like a mirror.
Triangle being reflected across a movable line
In more precise terms, a reflection across a line l maps every point A in the plane onto its image A' such that one of the following statements is satisfied.
  • If A is on the line l, then A and A' are the same point.
  • If A is not on the line l, then l is the perpendicular bisector of AA'.
Segment AA' intersects line ell perpendicularly, and line ell bisects segment AA'. Points B and B' coincide.

Like rotations and translations, reflections are rigid motions because they preserve the side lengths and angle measures. However, reflections can change the orientation of the preimage.

Exercises