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.

The opposite sides are equal in length and the angle between two adjacent sides is 90.

Step-by-step explanation:

Use the distance formula between two points.

Distance between A and B

AB =

AB =

Distance between C and D

CD =

CD =

Distance between C and D

BC =

BC =

Distance between D and A

DA =

DA =

Here, we observe that, AB = CD and BC = DA

Now to prove that they line AB is perpendicular to BC,

slope of AB = = \frac{1}{3}

Slope of BC = = -3

As the product of slope of AB and BC is -1 , so they are perpendicular to each other.

Now to prove that AD is perpendicular To DC

Slope of AD = = -3

Slope of DC = =\frac{1}{3}

As the product of slope of AD and DC is -1 , so they are perpendicular to each other.

So, it is a rectangle.