Let P = (5,1), and let Q be the reflection of P over the line y = 1/2x + 2. Find the coordinates of Q.

Question

I don't understand how to start? Should we draw perpendicular lines?

Answer 1

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)

Answer 2

thanks a lot