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.


3
1