Question

Points A(3, 1), B(12, –2) and C(0, 2) cannot be the vertices of a triangle.

विकल्प

• True

• False

Answer 1

This statement is True.

Explanation:

Coordinates of A = (x₁, y₁) = (3, 1)

Coordinates of B = (x₂, y₂) = (12, – 2)

Coordinates of C = (x₃, y₃) = (0, 2)

Area of ∆ABC = ∆ = `1/2[x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2)]`

Δ = `1/2 [3 - (2 - 2) + 12(2 - 1) + 0{1 - (- 2)}]`

Δ = `1/2 [3(- 4) + 12(1) + 0]`

Δ = `1/2 (- 12 + 12)` = 0

Area of ΔABC = 0

Since, the points A(3, 1), B(12, – 2) and C(0, 2) are collinear.

Therefore, the points A(3, 1), B(12, – 2) and C(0, 2) can’t be the vertices of a triangle.