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

False

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 = [x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]

∆ = [0( - 9 – 6) + 0(6 – 5) + 4(5 + 9)]

∆ = (0 + 0 + 3 × 14

∆ = 42/2 = 21 ≠ 0

As we can see the area of triangle formed by the points (0, 5), (0 - 9) and (3, 6) is not zero, and the points are only be collinear if area of a triangle, formed by its points is equals to the zero.

Hence, the points are non - collinear.