Analytic Geometry  Reflecting points over lines
posted by Knights on .
Let P = (5,1), and let Q be the reflection of P over the line y = 1/2x + 2. Find the coordinates of Q.
I don't understand how to start? Should we draw perpendicular lines?

Given (x,y) and a line y = ax + c we want the point (x', y') reflected on the line.
Set d:= (x + (y  c)*a)/(1 + a^2)
Then x' = 2*d  x
and y' = 2*d*a  y + 2c
This relies on the fact the the distance from (h,k) to the line ax+by+c = 0 is
ah+bk+c/√(a^2+b^2) 
thanks a lot