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Question
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
Options
- \[\frac{3}{4}\]
- \[\frac{4}{3}\]
- \[\frac{5}{3}\]
- \[\frac{3}{5}\]
Solution
We have three collinear points A (t,2t) ; B (-2,6) ; C (3,1).
In general if ` A (x_1 , y_1) ; B(x_2 , y_2 ); C (x_3 ,y_3)` are collinear then,
`x_1 (y_2 - y_3 ) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2 ) = 0`
So,
t(6- 1) - 2(1 -2r) + 3 (2t - 6) = 0
So,
5t + 4t + 6t -2 - 18 = 0
So,
15t = 20
Therefore,
` t = 4/3`
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