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,

x_{1} = 0, x_{2} = 0, x_{3} = 3 and

y_{1} = 5, y_{2} = - 9, y_{3} = 6

∵ Area of triangle = [x_{1}(y_{2} – y_{3}) + x_{2}(y_{3} – y_{1}) + x_{3}(y_{1} – y_{2})]

∆ = [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.

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