If the points A (1, 2), B (0, 0) and C (a, b) are collinear, then


Let the points are;

A = (x1, y1) = (1, 2)


B = (x2, y2) = (0, 0)


C = (x3, y3) = (a, b)


Area of ∆ABC= ∆ = 1/2


[x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]


=1/2 [1(0 - b) + 0(b - 2) + a(2 - 0)]


Δ=1/2 ( - b + 0 + 2a)=1/2(2a - b)


As, the points A (1, 2), B (0, 0) and C (a, b) are collinear, then area of ΔABC will be equals to the zero


Area of ΔABC = 0


1/2 (2a - b)


2a - b = 0


2a = b


Hence, the required relation is 2a = b

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