Question

Prove that the points (3, 2), (6, 3), (7, 6), (4, 5) are the vertices of a parallelogram. Is it a rectangle?

Answer 1

Given points are A(3, 2), B(6, 3), C(7, 6) and D(4, 5).

We need to prove that these are the vertices of a parallelogram.

We know that in the lengths of opposite sides are equal in a parallelogram.

Let us find the lengths of the sides.

We know that the distance between the points (x₁, y₁) and (x₂, y₂) is

Now,

⇒ CD = √10

⇒ DA = √10

We got AB = CD and BC = DA, these are the vertices of a parallelogram.

Now we find the lengths of the diagonals.

⇒ BD = √8

We got AC≠BD.

∴ The points doesn’t form a rectangle.