Please answer this question for I have a test coming up. My question is: Q. Given that the points (1,-1), (2,2) and (4,t) are collinear, find the...

If three points are collinear the area of the triangle formed by them is 0.

The formula to find area of a triangle formed by three points is

`1/2 [x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3(y_1 - y_2)] `

Now the given points `(1,-1), (2,2)` and `(4,t)` are colliner. So the area is 0

Lets take these points as `(x_1, y_1), (x_2, y_2), (x_3, y_3)` and substitute in the formula

`1/2 [1(2-t) + 2(t+1) + 4(-1 -2)] =0 `

`2 - t + 2t + 2 - 12 = 0 `

`t - 8 = 0 `

`t = 8 `

The required answer is t = 8