Question

Find the value of y for which the points A(-3, 9), B(2,y) and C(4,-5) are collinear.

Answer 1

Let `A(x_1=-3,y_1=9),B(x_2=2,y_2=y) and C(x_3=4, y_3=-5)` be the given points 

The given points are collinear if

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

`⇒(-3)(y+5)+2(-5-9)+4(9-y)=0`

`⇒ -3y-15-28+36-4y=0`

⇒7y = 36-43

⇒y = -1