State whether the following statements are true or false. Justify your answer.
The points $ (0,5),(0,-9) $ and $ (3,6) $ are collinear.

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

To do:

We have to find whether the given statement is true or false.

Solution:

We know that,

If the points \( (0,5),(0,-9) \) and \( (3,6) \) are collinear, then the area of triangle is 0.

Area of a triangle $=\frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right]$

Therefore,

Area of the given triangle $=\frac{1}{2}[0(-9-6)+0(6-5)+3(5+9)]$

$=\frac{1}{2}[0+0+3(14)]$

$=3(7)$

$=21$

The area of the triangle formed by the given points is not equal to 0.

Therefore, points \( (0,5),(0,-9) \) and \( (3,6) \) are not collinear.