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.