# Determine if the points (1, 5), (2, 3) and (- 2, - 11) are collinear

**Solution:**

The distance between the two points can be measured using the distance formula which is given by: Distance Formula = √ [(x_{2 - }x_{1})^{2} + (y_{2} - y_{1})^{2}]

Let the points (1, 5), (2, 3), and (- 2, - 11) be represented by the A, B, and C of the given triangle respectively

We know that the distance between the two points is given by the

Distance Formula = √ [(x_{2 - }x_{1})^{2} + (y_{2} - y_{1})^{2}] ....(1)

To find AB, the Distance between the Points A (1, 5) and B (2, 3), let x_{1} = 1, y_{1} = 5, x_{2} = 2, y_{2} = 3

∴ AB = √(1 - 2)² + (5 - 3)² (By Substituting in (1))

= √5

To find BC Distance between Points B (2, 3) and C (- 2, - 11), let x_{1} = 2, y_{1} = 3, x_{2} = - 2, y_{2} = - 11

Therefore, BC = √(2 - (- 2))² + (3 - (- 11))²

= √4² + 14² (By Substituting in the Equation (1))

= √16 + 196

= √212

To find AC Distance between Points A (1, 5) and C (-2, -11), let x_{1} = 1, y_{1} = 5, x_{2} = -2, y_{2} = -11

Therefore, CA = √(1- (- 2))² + (5 - (- 11))²

= √3² +16² (By Substituting in the Equation (1))

= √9 + 256

= √265

Since AB + AC ≠ BC and BC + AC ≠ AB and AB + BC ≠ AC Therefore, the points (1, 5), (2, 3), and (- 2, - 11) are not collinear.

**Video Solution:**

## Determine if the points (1, 5), (2, 3) and (- 2, - 11) are collinear

### NCERT Class 10 Maths Solutions- Chapter 7 Exercise 7.1 Question 3:

Determine if the points (1, 5), (2, 3) and (- 2, - 11) are collinear

Hence the points (1, 5), (2, 3) and (- 2, - 11) are not collinear