To continue ......
We know that the intersection of the two lines is ( -6/17, -2 10 /17) = (-6/17, -44/17)
This is the midpoint between A and A'
So......to find A' = (x, y) we have that
[-6 + x ] / 2 = -6/17 [ -4 + y ] / 2 = -44/17
-6 + x = -12/17 -4 + y = -88/17
x = -12/17 + 6 y = -88/17 + 4
x = -12/17 y = -20/17
x = 90/17
So A' = (90/17, -20/17)
Here's a graph : https://www.desmos.com/calculator/trsmplhqlg