Unizor - Geometry3D - Symmetry - Problems 1

Unizor - Creative Minds through Art of Mathematics - Math4Teens

Symmetry in 3D Space - Problems 1

Problem

Given are plane γ, point A outside it and point P lying on it: A∉γ; P∈γ.

Point B is symmetrical to point A relative to plane γ.
Point C is symmetrical to point A relative to point P.

Prove that points B and C are symmetrical relative to a line d perpendicular to plane γ and going through point P.