SOLUTION: Find all the value/s of t such that the points A(t-1, 2t-1), B(4, 1-2t) and C( -3, 3t+5) lie on the same line

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Find all the value/s of t such that the points A(t-1, 2t-1), B(4, 1-2t) and C( -3, 3t+5) lie on the same line      Log On


   

Question 767193: Find all the value/s of t such that the points A(t-1, 2t-1), B(4, 1-2t) and C( -3, 3t+5) lie on the same line
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
Find all the value/s of t such that the points A(t-1, 2t-1), B(4, 1-2t) and C( -3, 3t+5) lie on the same line
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A:
slope of AB = %28%281-2t%29+-+%282t-1%29%29%2F%284+-+%28t-1%29%29 = %28-4t%2B2%29%2F%28-t%2B5%29
slope of AC = %28%283t%2B5%29+-+%282t-1%29%29%2F%28-3-%28t-1%29%29 = %28t%2B6%29%2F%28-t-2%29
%28-4t%2B2%29%2F%28-t%2B5%29 = %28t%2B6%29%2F%28-t-2%29
%28-4t%2B2%29%28-t-2%29 = %28-t%2B5%29%28t%2B6%29
4t%5E2+%2B+6t+-+4 = -t%5E2+-t+%2B+30
5t%5E2+%2B+7t+-+34+=+0
(5t + 17)(t - 2) = 0
5t + 17 = 0 or t - 2 = 0
t = -17%2F5%29 OR 2