+1234 Let $B$ be the reflection of $A$ over the line $y = \frac{1}{2} x + 2$. Find the coordinates of $B$ if $A = (5,-1)$.
+129771 y = (1/2)x + 2
A line through (5, -1) that is perpendicular to the given line has the equation
y = -2(x - 5) -1
y = -2x + 9
The x intersection of these two lines is
(1/2)x + 2 = -2x + 9
(5/2)x = 7
x = 14/5 = 2.8
And the y value is -2(14/5) +9 = 17/5 = 3.4
From (5 , -1) we move [ (2.8-5) , (3.4 - - 1) ] = [ -2.2 , 4.4] to the intersection point
So B = [ 2.8 - 2.2 , 3.4 + 4.4] = (.6 , 7.8 )
