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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 
 \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}

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