In the diagram, WZ=StartRoot 26 EndRoot.

On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (negative 2, 4), point X is at (2, 4), point Y is at (1, negative 1), and point Z is at (negative 3, negative 1).

What is the perimeter of parallelogram WXYZ?

units
units
units
units

Answer:

[tex]P = 8 + 2\sqrt{26}[/tex]

Step-by-step explanation:

Given

[tex]W = (-2, 4)[/tex]

[tex]X = (2, 4)[/tex]

[tex]Y = (1, -1)[/tex]

[tex]Z = (-3,-1)[/tex]

Required

The perimeter

First, calculate the distance between each point using:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2[/tex]

So, we have:

[tex]WX = \sqrt{(-2- 2)^2 + (4-4)^2 } =4[/tex]

[tex]XY = \sqrt{(2- 1)^2 + (4--1)^2 } =\sqrt{26}[/tex]

[tex]YZ = \sqrt{(1- -3)^2 + (-1--1)^2 } =4[/tex]

[tex]ZW = \sqrt{(-3--2)^2 + (-1-4)^2 } =\sqrt{26}[/tex]

So, the perimeter (P) is:

[tex]P = 4 + \sqrt{26} + 4 + \sqrt{26}[/tex]

[tex]P = 8 + 2\sqrt{26}[/tex]

Answer:

its D.

Step-by-step explanation:

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