Q. 213.7( 3 Votes )

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

Answer :

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 (x_{1}, y_{1}) and (x_{2}, y_{2}) is .

Now,

⇒ AB = √10

⇒ BC = √10

⇒ 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.

⇒ AC = √32

⇒ BD = √8

We got AC≠BD.

∴ The points doesn’t form a rectangle.

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