Q13 of 149 Page 15

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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