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