If three points (x1, y1), (x2, y2), (x3, y3) lie on the same line, prove that


Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3)


= |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|


Given that all points are collinear.


area = 0


x1(y2-y3)+x2(y3-y1)+x3(y1-y2) = 0


Dividing by x1 x2 x3,


+ + = 0



Hence proved.


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