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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

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by anudeepd2

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by anudeepd2

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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

⇒

⇒-5/(k-1)= -1

⇒k-1 = 5

k = 6__ANSWER__

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

⇒

⇒-5/(k-1)= -1

⇒k-1 = 5

k = 6

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