Prove that the points (a, 0), (0, b) and (1, 1) are collinear if , 1a+1b=1.
If 3 points are collinear, then the area of the triangle formed by them is zero.
Area of triangle = 12|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|=0
⇒x1(y2−y3)+x2(y3−y1)+x3(y1−y2)=0
⇒a(b−1)+0(1−0)+1(0−b)=0
⇒a+b=ab
⇒1a+1b=1