Question

Find c such that (−3,−8), (−7,−6), and (c,4) lie on a line.

Answer 1

If the 3 points are collinear, then the slopes of all line segments connecting the points are the same.

Thus,

-6 - (-8) 2
m = ------------- = -------- = -1/2
-7 - (-3) -4

Then the following must be true:

4-(-6) 10
-1/2 = ------------ = ---------
c - (-7) c + 7

Cross multiplying, -(c+7) = 20, and c+7 = -20, so that c = -27