Question

Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.

Answer 1

In the parallelogram opposit sides are equal and also in the rectangle both sides are parallel

Answer 2

Concept

A parallelogram is 2 dimensional figure which have two sides parallel to each other and a rectangle is a 2 dimensional figure which have a length and breadth and have two corresponding sides equal.

Given

Points of ABCD are A(-3,1), B(3,3), C(4,0), D(-2,-2)

To find

Prove that the parallelogram is a rectangle.

Explanation

With the help of the points we can find the length of a side and in a rectangle two corresponding sides should be equal to each other.

AB=$\sqrt{(3+3)^{2}+(3-1)^{2} }$

=$\sqrt{6^{2}+2^{2} }$

=$\sqrt{36+4}$

=$\sqrt{40}$ units

BC=$\sqrt{(-3^{2}+(4-3)^{2} }$

=$\sqrt{10}$ units

CD=$\sqrt{(-2)^{2}+(-6)^{2} }$

=$\sqrt{40}$ units

AD=$\sqrt{(-3^{2} +1^{2} }$

=$\sqrt{10}$ units

We can see that AB=BC and CD=AD.

Hence the parallelogram ABCD is a rectangle.

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