By using the concept of equation of a line, prove that the three points (3, 0), (- 2, - 2) and (8, 2) are collinear.

Solution:

In order to show that the points (3, 0), (- 2, - 2) and (8, 2) are collinear, it suffices to show that the line passing through points (3, 0) and (- 2, - 2) also passes through point (8, 2).

The equation of the line passing through points (3, 0) and (- 2, - 2) is

(y - 0) = (-2 - 0)/(- 2 - 3) (x - 3)

y = (- 2)/(- 5) (x - 3)

5 y = 2x - 6

2x - 5 y - 6 = 0

It is observed that at x = 8, y = 2

LHS = 2 (8 )- 5 (2) - 6

= 16 - 10 - 6

= 0

= RHS

Therefore, the line passing through points (3, 0) and (- 2, - 2) also passes through point (8, 2).

Hence, points (3, 0), (-2, -2) and (8, 2) are collinear

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 20

By using the concept of equation of a line, prove that the three points (3, 0), (- 2, - 2) and (8, 2) are collinear

Summary:

The points (3, 0), (- 2, - 2), and (8, 2) are proved to be colinear by the concept of the equation of a line