Question 767193
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 = {{{((1-2t) - (2t-1))/(4 - (t-1))}}} = {{{(-4t+2)/(-t+5)}}}
slope of AC = {{{((3t+5) - (2t-1))/(-3-(t-1))}}} = {{{(t+6)/(-t-2)}}}
{{{(-4t+2)/(-t+5)}}} = {{{(t+6)/(-t-2)}}}
{{{(-4t+2)(-t-2)}}} = {{{(-t+5)(t+6)}}}
{{{4t^2 + 6t - 4}}} = {{{-t^2 -t + 30}}}
{{{5t^2 + 7t - 34 = 0}}}
(5t + 17)(t - 2) = 0
5t + 17 = 0 or t - 2 = 0
t = {{{-17/5)}}} OR 2