Question 1203671
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Find C such that (10,-1), (-4,10), and (C,-6) lie on a line. What is the C value?
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<pre>
Write an equation saying that the slope of the segment PQ, where P= (10,-1), Q= (-4,10),
is the same as the slope of the segment QR, where R= (C,-6).

The slope of the segment PQ is  {{{(10-(-1))/(-4-10)}}} = {{{11/(-14)}}} = {{{-11/14}}}.

The slope of the segment QR is  {{{(-6-10)/(C-(-4))}}} = {{{(-16)/(C+4)}}}.


So, the equation is

    {{{-16/(C+4)}}} = {{{-11/14}}}.


It implies

    {{{16/(C+4)}}} = {{{11/14}}}

    16*14 = 11*(C+4)

     224  = 11C + 44

     224 - 44 = 11C

        180   = 11C

         C    = {{{180/11}}} = 16{{{4/11}}}.    <U>ANSWER</U>
</pre>

Solved.