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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Area of triangle =21[x1(y2−y1)+x2(y3−y1)+x3(y1−y3)]
=21[x(7−5)+5(5−y)−4(4−7)]
Given A,B and C are collinear, then area of triangle must be zero.
∴21[x(7−5)+5(5−y)−4(4−7)]=0
⇒21[2x−25+5y−4y+25]=0
⇒21(2x+y+3)=0
Then, relation between x and y is 2x+y+3=0
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