Let A = (6,2), and let B be the reflection of A over the line y = 2x + 5 . Find the coordinates of B.
+128460 A line perpendicular to the given one has a slope of -1/2
And the equation of this line through (6,2) is
y= (-1/2) ( x - 6) + 2
y =(-1/2) x + 3 + 2
y =(-1/2) x + 5
To find the x coordinate of the intersection of these lines :
2x + 5 = (-1/2x) + 5
x = 0
y= 5
And this is the midpoint of (6,2) and its reflected point
To get from (6,2) to (0,5) we had to go to the left 6 and up 3
Applying the same movement from (0,5) we get the reflected point B = ( -6, 8)
