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

Equation for collinear = $\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))$

$0=-3(b+5)+a(-5-9)+4(9-b)$

$7b+14a-21=0$

$b+2a=3$

$1-a+2a=3$

$a=2$

$b=-1$