If the points (-1, t -1), (t, t – 3) and (t – 6, 3) lie on the same straight line, find the values of t.
-
A.
t = -2 and 3 -
B.
t = 2 and -3 -
C.
t = 2 and 3 -
D.
t = -2 and -3
Correct Answer: Option C
Explanation
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 = frac{(t-3) – (t-1)}{t – (-1)} = frac{3 – (t-3)}{(t-6) – t} = frac{3 – (t-1)}{(t-6) – (-1)})
Taking any two of the equations above, solve for t.
(frac{t – 3 – t + 1}{t + 1} = frac{6 -t}{-6})
(12 = (6 – t)(t + 1))
(-t^{2} + 5t + 6 – 12 = 0 implies t^{2} – 5t + 6 = 0)
Solving, we have t = 2 and 3.