SOLUTION: The points (3,2), (5,k) and (-k,4) are collinear. Find the possible values of k. Any help appreciated!

Algebra ->  Coordinate-system -> SOLUTION: The points (3,2), (5,k) and (-k,4) are collinear. Find the possible values of k. Any help appreciated!      Log On


   

Question 1045277: The points (3,2), (5,k) and (-k,4) are collinear. Find the possible values of k.
Any help appreciated!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28k-2%29%2F%285-3%29=%284-k%29%2F%28-k-5%29=%284-2%29%2F%28-k-3%29, to help you start...


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So what did you do? That combined equation means that the slopes are equal. The points must be on the same line. You have also the additional equation, %28k-2%29%2F%285-3%29=%284-2%29%2F%28-k-3%29.


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Just try this much of the combination equation:
%28k-2%29%2F%285-3%29=%284-k%29%2F%28-k-5%29
%28k-2%29%28-k-5%29=%284-k%29%285-3%29
-1%28k-2%29%28k%2B5%29=2%284-k%29
-1%28k%5E2%2B3k-10%29=8-2k
-k%5E2-3k%2B10=-2k%2B8
-k%5E2-k%2B2=0
k%5E2%2Bk-2=0
%28k%2B2%29%28k-1%29=0
system%28k=-2%2Cor%2Ck=1%29

Try another part of the combination equation:
%284-k%29%2F%28-k-5%29=%284-2%29%2F%28-k-3%29
%284-k%29%2F%28k%2B5%29=%284-2%29%2F%28k%2B3%29
%284-k%29%2F%28k%2B5%29=2%2F%28k%2B3%29
%284-k%29%28k%2B3%29=2%28k%2B5%29
%28k-4%29%28k%2B3%29=-2%28k%2B5%29
k%5E2-k-12=-2k-10
k%5E2%2Bk-2=0-----------which is the same equation resulted from the first tried part of the combined equation.

The possible values for k are highlight%28system%28k=-2%2Cor%2Ck=1%29%29.