Question

Prove that the points A (4, 3), B (6, 4), C (5, −6) and D (3, −7) in that order are the vertices of a parallelogram.

Answer 1

Given points A (4, 3), B (6, 4), C (5, −6) and D (3, −7).

We have to prove that these points form vertices of a parallelogram.

The above four points will form 4 line segments.

AB, BC, CD, AD

We know that length of a line segment having coordinates

Therefore

It can be seen that AB = CD , BC = AD

Since opposite sides are equal, ABCD is a parallelogram

Hence proved.