# 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.

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We know that For the points to be collinear;

PQ + QR = PR

=>

m(PQ) + m(QR )= m(PR)

This is the distance formula

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}