the answer
the full question is
If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) form two line segments, and AB ⊥ CD, which condition needs to be met to prove AB ⊥ CD?
let be A(x1, y1)B(x2, y2) the first line, and C(x3, y3) D(x4, y4) the second
the slope of the first line is m = y2 -y1 / x2 - x1
the slope of the second line is m' = y4 -y3 / x4 - x3
so the condition needs to be met to prove AB ⊥ CD is
y2 -y1 y4 -y3
m x m' = --------- x ------------ = -1
x2 - x1 y4 -y3
