Question

Find the perimeter of WXYZ. Round to the nearest tenth if necessary.

Answer 1

22.4

Explanation:

X(2,3)

W(-4,2)

Z(-3,-3)

Y(1,-4)

distance between two points :

`\sqrt{ {(x1 - x2)}^(2) + {(y1 - y2)^(2) } }`

XW = sqrt(37)

XY= sqrt(50)

WZ= sqrt(26)

YZ= sqrt(17)

xw+xy+wz+yz = 22.37

Answer 2

The perimeter of WXYZ is approximately 22.4 (rounded to the nearest tenth) (Option D).

How to find the perimeter of a figure?

To find the perimeter of the quadrilateral WXYZ, you can use the distance formula to calculate the length of each side and then add them up.

The distance formula between two points
`(x_1, y_1)` and
`(x_2, y_2)` is given by:

`d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let's calculate the distances for each side of WXYZ:

1. Distance between W(-4,2) and X(2,3):

`WX = √((2 - (-4))^2 + (3 - 2)^2)`

`WX = √(37)`

2. Distance between X(2,3) and Y(1,-4):

`XY = √((1 - 2)^2 + ((-4) - 3)^2)`

`XY = √(50)`

3. Distance between Y(1,-4) and Z(-3,-3):

`YZ = √(((-3) - 1)^2 + ((-3) - (-4))^2)`

`YZ = √(17)`

4. Distance between Z(-3,-3) and W(-4,2):

`ZW = √(((-4) - (-3))^2 + (2 - (-3))^2)`

`ZW = √(26)`

Now, add up the distances to find the perimeter:

Perimeter = WX + XY + YZ + ZW

Perimeter =
`√(37) + √(50) + √(17) + √(26)`

Calculating this sum will give you the perimeter of WXYZ. Let me perform the calculation:

Perimeter ≈ 6.08 + 7.07 + 4.12 + 5.10

Perimeter ≈ 22.4 (Option D).