Without using distance formula, show that points (- 2, - 1), (4, 0), (3, 3) and (- 3, 2) are vertices of a parallelogram

Solution:

Let points (- 2, - 1), (4, 0), (3, 3) and (- 3, 2) be respectively denoted by A, B, C and D.

Slope of AB = (0 + 1)/(4 + 2) = 1/6

Slope of CD = (2 - 3)/( -3 - 3) = - 1/- 6 = 1/6

Therefore, Slope of AB = Slope of CD

Hence, AB and CD are parallel to each other.

Now,

Slope of BC = (3 - 0)/(3 - 4) = 3/- 1 = - 3

Slope of AD = (2 + 1) / (-3 + 2) = 3/(-1) = -3

Therefore, Slope of BC = Slope of AD Hence, BC and AD are parallel to each other.

Therefore, both pairs of the opposite sides of quadrilateral ABCD are parallel.

Hence, ABCD is a parallelogram.

Thus, points (- 2, - 1), (4, 0), (3, 3) and (- 3, 2) are the vertices of a parallelogram

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.1 Question 9

Without using distance formula, show that points (- 2, - 1), (4, 0), (3, 3) and (- 3, 2) are vertices of a parallelogram

Summary:

The points (- 2, - 1), (4, 0), (3, 3) and (- 3, 2) which are respectively denoted by A, B, C, and D form the vertices of a parallelogram