Posted by Knights on Monday, March 4, 2013 at 10:51am.
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?

Analytic Geometry  Reflecting points over lines  Steve, Monday, March 4, 2013 at 12:15pm
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)

Analytic Geometry  Reflecting points over lines  Knights, Monday, March 4, 2013 at 6:21pm
thanks a lot
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