Question

Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates (1$\frac{1}{2}$, 2$\frac{1}{4}$) and (−2$\frac{-1}{4}$, k). What value of k makes these segments perpendicular?

Answer 1

Given : Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates(1 1/2,  2 1/4) and (−21/4, k).

To Find : What value of k makes these segments perpendicular

Solution:

Endpoints of segment MN have coordinates (0, 0), (5, 1)

slope of MN = ( 1 - 0)/(5 - 0)  = 1/5

The endpoints of segment AB have coordinates (1 1/2,  2 1/4) and (−21/4, k).

Slope of AB  =  ( k - 9/4) /(-9/4 - 3/2)  = (4k - 9)/(-15)

MN & AB will be perpendicular iff

slope of MN  x Slope of AB = - 1

=> (1/5) ( (4k - 9)/(-15)) = - 1

=> 4k - 9  = 75

=> 4k = 84

=> k = 21

Value of k = 21

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