If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie o...
If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie on the same straight line, find the values of t.
t = -2 and 3
t = 2 and -3
t = 2 and 3
t = -2 and -3
Correct answer is C
For collinear points (points on the same line), the slopes are equal for any 2 points on the line.
Given (-1, t - 1), (t, t - 3), (t - 6, 3),
slope=(t−3)−(t−1)t−(−1)=3−(t−3)(t−6)−t=3−(t−1)(t−6)−(−1)
Taking any two of the equations above, solve for t.
t−3−t+1t+1=6−t−6
12=(6−t)(t+1)
−t2+5t+6−12=0⟹t2−5t+6=0
Solving, we have t = 2 and 3.
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