Let B be the reflection of A over the line $y = \frac{1}{2} x + 2$. Find the coordinates of B.
+130081 The slope of the line perpendicular to the given line is -2
A line with this slope going through A has the equation
y = -2 ( x -3) + 1
y = -2x + 7
Setting the two equations equal to find the x intersection of these lines we have
(1/2)x + 2 = -2x + 7
(5/2)x = 5
x = 5 ( 2/5) = 2
And the y intersection = -2(2) + 7 = 3
So the intersection pt is (2,3)
Using the midpoint rule we can find the coordinates of B as
[ 3 + x] / 2 = 2 ⇒ 3+ x = 4 ⇒ x =1
[1 + y] / 2 = 3 ⇒ 1 + y = 6 ⇒ y = 5
So
B = ( 1 , 5)
