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

Q.No. 9 of Exercise 10.1 of Class 11th

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

Sol :

The given points are A(-2,-1), B(4,0), C(3,3), D(-3,3).

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

Slope of DC = 3-2/3-(-3) = 1/3+3 = 1/6

Here              Slope of AB = Slope of DC
Therefore     AB and DC are Parallel  

Similarly

Slope of AD = 2-(-1)/-3-(-2) = 2+1/-3+2 = 3/-1
Slope of BC = 3-0/3-4 = 3/-1

Here             Slope of AD = Slope of BC
Therefore    AD and BC are Parallel

Hence         ABCD are Parallelogram