Question 1010002: Find two values of k such that the points (-3,4), (0,k), and (k,10) are collinear.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find two values of k such that the points (-3,4), (0,k), and (k,10) are collinear.
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Look at the slopes::
1st point to 3rd point::
(k-4)/(0+3) = (10-4)/(k+3)
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Cross multiply::
k^2 - k - 12 = 3*6
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k^2 - k - 30 = 0
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(k-6)(k+5) = 0
k = 6 or k = -5
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Cheers,
Stan H.
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Answer by MathLover1(20849)  (Show Source):
You can put this solution on YOUR website! Find two values of k such that the points ( , ), ( , ), and (, ) are collinear.
the points are collinear if they lie on same line
use the slope of a line to find
for the points (,), (,),
 .............eq.1
for (,), and (,)
 ............eq.2
from eq.1 and eq.2 we have
 ............cross multiply
 ...........factor completely
solutions:
so, the points (,), (, ), and (,) are collinear
and the points (,), (, ), and (,) are collinear
now find slope
.............eq.1 if
.............eq.1 if
so, there are  possible lines and they are
 and
we need y-intercepts 
 use one point : (,)
 and
 use one point : (,)
so, the line contains points the points (,), (,), and (,)
and the line contains points the points (,), (,), and (,)
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