SOLUTION: The line segment drawn from A(k, 3) to B(4, 1) is perpendicular to the segment drawn from C(-5, -6) to D(4, 1). Find the value of k.

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Question 1191647: The line segment drawn from A(k, 3) to B(4, 1) is perpendicular to the segment drawn from C(-5, -6) to D(4, 1). Find the value of k.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
The line segment drawn from A(k, 3) to B(4, 1) is perpendicular to the segment
drawn from C(-5, -6) to D(4, 1). Find the value of k.
~~~~~~~~~~~~~~~~~~ 

Segment  CD  has the slope   =  = .


Segment  AB  has the slope   =  = 



In order for the segments be perpendicular, the slopes must be negative reciprocal   = - ,  or

     = .


From this proportion

    2*7 = 9*(4-k),

or

    14 = 36 - 9k

    9k = 36 - 14

    9k =    22

     k =  = 2 .    ANSWER

Solved.



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