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Question

Show that the points P(a,b+c),Q(b,c+a) and R(c,a+b) are collinear.

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Solution

Given: P(a,b+c),Q(b,c+a) and R(c,a+b)

We know that, the points P, Q and R will be collinear if slope of PQ and QR is the same.

Slope =y2y1x2x1

Slope of PQ=c+abcba=abba=1

Slope of QR=a+bcacb=bccb=1

Slope of PQ = slope of QR

So, the points P, Q and R are collinear.

Hence proved.

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