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

We know that For the points to be collinear;

PQ + QR = PR

=>

m(PQ) + m(QR )= m(PR)
This is the distance formula 
$\sqrt{(y2-y1)^2 +(y2-y1)^2 }$

Apply this to every line segment

Now with the help of the equation a + b = 1

Evaluate the first equation by taking a = 1-b
Now after solving for b you find a

You will get {a = 2 b = -1}