Unizor - Geometry3D - Plane Reflection

Unizor - Creative Minds through Art of Mathematics - Math4Teens

Plane reflection in three-dimensional space assumes the existence of a fixed plane of reflection.

To construct a point A' reflectively symmetrical to a given point A relatively to a plane of reflection γ, we have to drop a perpendicular from point A onto plane γ and extend it beyond the base point by the same length.

Based on this construction, it's easily observed that the process is reversible. If we start from point A', drop a perpendicular to the same plane γ and extend it by the same length, we will arrive to the original point A. We can say, therefore, that the process of reflection is reflexive, that is, if point A' is a reflective image of point A relative to plane γ, then point A is a reflective image of point A' relative to the same plane γ.

Theorem 1
A reflectively symmetrical counterpart of a straight line is a straight line.

Theorem 2
A reflectively symmetrical counterpart of a plane is a plane.