# Symmetry of a 3D point A by a line made of 2 points B and C

Given a point A of coordinates $$(a_1,b_1,c_1)$$ and two points $$B(x_1,y_1,z_1)$$ and $$C (x_2,y_2,z_2)$$

What are the coordinates of $$D(a_2,b_2,c_2)$$ symmetry of A by the line BC?

If $$D$$ is symmetry of $$A$$ by line $$BC$$, then $$ABDC$$ is a parallelogram.
$$\vec{A}+\vec{D}=\vec{B}+\vec{C}$$