Question

For what value of x are the points A(-3, 12), B(7, 6) and C(x, 9) collinear.

Answer 1

A(-3,12) ,B (7,6) and C(x,9) are the given points. Then:

`(x_1=-3,y_1=12) , (x_2=7,y_2=6) and (x_3= x, y_3=9)`

It is given that points A, B and C are collinear. Therefore,

`x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)=0`

`⇒ (-3)(6-9)+7(9-12)+x(12-6)=0`

`⇒(-3)(-3)+7(-3)+x(6)=0`

`⇒ 9-21+6x=0`

`⇒ 6x-12=0`

`⇒ 6x =12`

`⇒ x = 12/6=12`

Therefore, when  x =2 , the given points are collinear