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Question

Find the relation between x and y if the points A(x,y),B(5,7) and C(4,5) are collinear.

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Solution

Area of triangle =12[x1(y2y1)+x2(y3y1)+x3(y1y3)]
=12[x(75)+5(5y)4(47)]

Given A,B and C are collinear, then area of triangle must be zero.
12[x(75)+5(5y)4(47)]=0

12[2x25+5y4y+25]=0

12(2x+y+3)=0

Then, relation between x and y is 2x+y+3=0

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