Foot of the perpendicular from a given line.

Let, A(x₂,y₂) is the feet of a perpendicular from the point B(x₁,y₁) of the straight line ax + by + c = 0 then,

(x₂-x₁)/a = (y₂-y₁)/b =-2(ax₁ +by₁ +c)/(a²+b²).

If image of "A" w.r.t the line mirror ax + by + c = 0 is "B" then also the above is true.