# Are the set of points A (3, 0), B(-2, 10), C(0, 5) are collinear?

##### 1 Answer
Aug 5, 2018

The given points are non collinear.

#### Explanation:

Here ,

$A \left(3 , 0\right) , B \left(- 2 , 10\right) , C \left(0 , 5\right) .$

Using Distance Formula:

$A B = \sqrt{{\left(3 + 2\right)}^{2} + {\left(0 - 10\right)}^{2}} = \sqrt{25 + 100} = \sqrt{125} = 5 \sqrt{5}$

$B C = \sqrt{{\left(- 2 - 0\right)}^{2} + {\left(10 - 5\right)}^{2}} = \sqrt{4 + 25} = \sqrt{29}$

$A C = \sqrt{{\left(3 - 0\right)}^{2} + {\left(0 - 5\right)}^{2}} = \sqrt{9 + 25} = \sqrt{29}$

Now,

$A B + B C \ne A C ,$

$B C + A C \ne A B ,$

$A B + A C \ne B C$

So, the given points are non collinear.