Question

If the points P(–3, 9), Q(a, b) and R(4, –5) are collinear and a + b = 1, find the values of a and b.

Answer 1

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

The given pots are collinear if

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

`⇒ (-3)(b+5)+a(-5-9)+4(9-b)=0`

`⇒-3b-15-14a+36-4b=0`

⇒ 2a + b = 3

Now solving 1 a +b = 1 and 2a+ b = 3, we get a =2 and b= -1.

Hence, a = 2 and b = -1.