Question

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

पर्याय

• a = b

• a = 2b

• 2a = b

• a = – b

Answer 1

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

Explanation:

Let the given points are A = (x₁, y₁) = (1, 2),

B = (x₂, y₂) = (0, 0) and C = (x₃, y₃) = (a, b).

∵ Area of ΔABC

Δ = `1/2[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]`

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

= `1/2(-b + 0 + 2a)`

= `1/2(2a - b)`

Since, the points A(1, 2), B(0, 0) and C(a, b) are collinear, then area of ΔABC should be equal to zero.

i.e., Area of ΔABC = 0

⇒ `1/2(2a - b)` = 0

⇒ 2a – b = 0

⇒ 2a = b

Hence, the required relation is 2a = b.