Question 1191647
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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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<pre>
Segment  CD  has the slope  {{{m[CD]}}} = {{{(1-(-6))/(4-(-5))}}} = {{{7/9}}}.


Segment  AB  has the slope  {{{m[AB]}}} = {{{(1-3)/(4-k)}}} = {{{-2/(4-k)}}}



In order for the segments be perpendicular, the slopes must be negative reciprocal  {{{m[CD]}}} = - {{{1/m[AB]}}},  or

    {{{7/9}}} = {{{(4-k)/2}}}.


From this proportion

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

or

    14 = 36 - 9k

    9k = 36 - 14

    9k =    22

     k = {{{22/9}}} = 2 {{{4/9}}}.    <U>ANSWER</U>
</pre>

Solved.