Point A is reflected over the line shown below to point B. Find the coordinates of B.
Write your answer as an ordered pair (x,y).
The line is y = x + 3, and A = (7,1).
The given line has a slope of 1
A perpendicular line to this passing through (7,1) has the equation
y = - ( x -7) + 1
y = -x + 8
The x intersection of these two lines is
x + 3 = -x + 8
2x = 5
x =5/2
And y = (5/2) + 3 = 11/2
From (7,1) to ( 5/2, 11/2) we went back to the left 7 -5/2 = 9/2 unirs
And 11/2 - 1 = 9/2 units up
So
B = [ 5/2 - 9/2, 11/2 + 9/2] = ( -2, 10 )