Prove that the points (a, 0), (0, b) and (1, 1) are collinear if,

Let three given points be A(a,0), B(0,b) and C(1,1).


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


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


Area of ∆ABC


= |a(b – 1) + 1(0 -b)|


= | ab – a –b|


Here given that


= 1


a + b = ab


Now,


Area of ∆ABC


= | ab - (a + b)|


= | ab – ab|


= | 0 |


= 0 sq. units


We know that if area enclosed by three points is zero, then points are collinear.


Hence, given three points are collinear.


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