Question

If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =

Options

• \[\frac{3}{4}\]

   

• \[\frac{4}{3}\]

   

• \[\frac{5}{3}\]

   

• \[\frac{3}{5}\]

   

Answer 1

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`