Answer :

The perimeter of square WXYZ is approximately 25.6 units, calculated by summing the distances between consecutive vertices using the distance formula.

To find the perimeter of the square WXYZ, we need to calculate the distance between consecutive vertices and then sum these distances.

The distance between two points (x₁, y₁) and (x₂, y₂) in the coordinate plane can be determined using the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

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

1. Distance between W(-4,0) and X(1,4)

WX = √((1 - (-4))² + (4 - 0)²) = √(5² + 4²) = √(25 + 16) = √41

2. Distance between X(1,4) and Y(5,-1):

XY = √((5 - 1)² + (-1 - 4)²) = √(4² + (-5)²) = √(16 + 25) = √41

3. Distance between Y(5,-1) and Z(0,-5):

YZ = √((0 - 5)² + (-5 - (-1))²) = √((-5)² + (-4)²) = √(25 + 16) = √41

4. Distance between Z(0,-5) and W(-4,0):

ZW = √((-4 - 0)² + (0 - (-5))²) = √((-4)² + 5²) = √(16 + 25) = √41

Now, summing up these distances gives the perimeter of the square:

Perimeter = WX + XY + YZ + ZW = 4√41

Approximating this value, we get:

Perimeter ≈ 4 × 6.4 ≈ 25.6

So, the correct answer is B) 25.6 units.

The question probable may be:

X(1,4) Y(5,-1)

Z(0,-5) W(-4,0)

Look at the square WXYZ on the coordinate plane. What is the perimeter of the square WXYZ?

A) 20units

B) 25.6units

C) 32units

D) 40.9units

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Rewritten by : Barada