Question

If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =

Options

• −3

• 7

• 2

• -2

Answer 1

We have three collinear points A(1,2) ;B(-5,6) ;C(a, - 2).

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,

1(6 + 2) - 5(- 2-2)+ a (2 -6 ) = 0

So,

-4a + 8 + 20 = 0

Therefore,

 a = 7