Question

The points (0, 5), (0, –9) and (3, 6) are collinear.

विकल्प

• True

• False

Answer 1

This statement is False.

Explanation:

The points are collinear if area of a triangle formed by its points is equals to the zero.

Given,

x₁ = 0, x₂ = 0, x₃ = 3 and y₁ = 5, y₂ = – 9, y₃ = 6

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

Δ = `1/2[0(-9 - 6) + 0(6 - 5) + 4(5 + 9)]`

Δ = `1/2(0 + 0 + 3 xx 14)`

Δ = `42/2 = 21 ≠ 0`

From the above equation, it is clear that the points are not collinear.