Theorem 4.9: If   R   is a reflection, then   R(R(A)) = A   for all points   A   in the plane.

Proof: Let   F   be the foot of the point   A   in the line about which the plane is reflected. By Theorem 4.6,

R(A) = 2F - A

so

R(R(A)) = 2F - (2F - A) = A

next theorem (4.10)