(y - yo) = m.(x - xo)
Where (x, y) and (xo, yo) are points of a line and m his slope
If both lines have m equal they are parallels, if they are the opposite inverse they are perpendicular
So, let's see.
line which pass by (-52, -18) and (-29, 53)
(53 - (-18)) = m.(-29 - (-52))
53 + 18 = m.(-29 + 52)
71 = m.(23)
m = 71/23
line which pass by (90, 33) and (19, 56)
(56 - 33) = m.(19 - 90)
23 = m.(-71)
m = -23/71
As we see, 71/23 and -23/71 are opposite inverses of one another, so they are perpendicular lines.
