If a(x1, y1), b(x2, y2), c(x3, y3), and d(x4, y4) form two line segments, and , which condition needs to be met to prove ?

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

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