Question

Show that A (-2,1) , B (0,3) , C (2,1) and D(0,-1) are the verticles of a parallelogram.

Answer 1

Let the coordinates of following points are as follows:
A (-2,1) , B (0,3) , C (2,1) and D(0,-1)


We know that slope of a line = $\frac{y_2-y_1}{x_2-x_1}=\frac{y_1-y_2}{x_1-x_2}$
Now, we have:

Slope of AB =$\frac{1-3}{-2-0}=1$ …(i)

Slope of BC = $\frac{3-1}{0-2}=-1$ …(ii)

Slope of AD = $\frac{1-(-1)}{-2-0}=-\frac{2}{2}=-1$ …(iii)

Slope of DC = $\frac{1-(-1)}{2-0}=\frac{2}{2}=1$ …(iv)

From (i) and (iv), slope of AB = slope of DC
i.e., AB is parallel to DC.
Similarly, from (ii) and (iii), slope of BC = slope of AD
i.e., BC is parallel to AD.
Here, both pairs of the opposite sides are parallel.
∴ ABCD is a parallelogram.