Question

For what value of y, are the points P(1, 4), Q(3,y) and R(-3, 16) are collinear ?

Answer 1

P(1, 4), Q(3,y) and R(-3, 16) are the given points. Then:

`(x_1=1, y_1=4), (x_2=3, y_2=y) and (x_3 =-3, y_3 =16)`

It is given that the points P, Q and R are collinear. Therefor,

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

`⇒ 1(y-16)+3(16-4)+(-3)(4-y)=0`

`⇒ 1(y-16)+3(12)-3(4-y)=0`

`⇒ y-16+36-12+3y=0`

`⇒8+4y=0`

`⇒ 4y =-8/4=-2`

When, y=-2  the given points are collinear.