Question

If A(2,-5),B(-2,5),C(k,3) and D(1,1) are four points such that AB and CD are pependicular to each other, find k

Answer 1

so we know then when two lines are perpendicular then the product of the slopes of two lines = -1

m x m₁ = -1   ........ i

so slope of AB m = (5 + 5)/(-2 - 2) = - 5/2
slope of CD m₁ = (3 - 1)/(k-1) = 2/(k - 1)

using i 

⇒$\frac{-5}{2}*\frac{2}{(k - 1)}=-1$

⇒-5/(k-1)= -1
⇒k-1 = 5
k = 6 ANSWER

Answer 2

If AB and CD are perpendicular then
slope of AB *slope of CD = -1
5+5/-2-2 * 1-3/1-k = -1
10/-4 * -2/1-k = -1
5/-2*-2/1-k=-1
5/1-k=-1
5=k-1
k=5+1
k=6