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(52781) About Me  (Show Source):
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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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Segment  CD  has the slope  m%5BCD%5D = %281-%28-6%29%29%2F%284-%28-5%29%29 = 7%2F9.


Segment  AB  has the slope  m%5BAB%5D = %281-3%29%2F%284-k%29 = -2%2F%284-k%29



In order for the segments be perpendicular, the slopes must be negative reciprocal  m%5BCD%5D = - 1%2Fm%5BAB%5D,  or

    7%2F9 = %284-k%29%2F2.


From this proportion

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

or

    14 = 36 - 9k

    9k = 36 - 14

    9k =    22

     k = 22%2F9 = 2 4%2F9.    ANSWER

Solved.