Question

How do you prove that A(-2,2), B(1,4), C(2,8) and D(-1,6) is a parallelogram?

Answer 1

Please see below.

Explanation:

As opposite sides of a parallelogram are parallel,

we need to prove that `AC` and `BD` are parallel as well as `AD` and `BC` are parallel. Further slopes of parallel lines are equal.

As slope of a line joining two points `(x_1,y_1)` and `(x_2,y_2)` is given by `(y_2-y_1)/(x_2-x_1)` and therefore

Slope of `AB` is `(4-2)/(1-(-2))=2/3`

slope of `BC` is `(8-4)/(2-1)=4/1`

slope of `CD` is `(6-8)/(-1-2)=(-2)/(-3)=2/3` and

slope of `DA` is `(6-2)/(-1-(-2))=4/1`

and as `AC` and `BD` are parallel as well as `AD` and `BC` are parallel,

`ABCD` is a parallelogram.