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

Let the points are;

A = (x_{1}, y_{1}) = (1, 2)

B = (x_{2}, y_{2}) = (0, 0)

C = (x_{3}, y_{3}) = (a, b)

∵ Area of ∆ABC= ∆ = 1/2

[x_{1}(y_{2} – y_{3}) + x_{2}(y_{3} – y_{1}) + x_{3}(y_{1} – y_{2})]

∴ ∆ =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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