Question

Look at the square WXYZ on this coordinate plane.
graph shows 4 points x(1,4) y(5,-1) z(0,-5) w(-4,0)




Which measure is closest to the perimeter of the square WXYZ?

(1 point)
Responses

20 units
20 units

40.9 units
40.9 units

32 units
32 units

25.6 units

Answer 1

To find the perimeter of square WXYZ, we first need to determine the length of one side of the square. Given the points W(1, 4), X(5, -1), Y(0, -5), and Z(-4, 0), we can calculate the distance between two adjacent points.

Let's find the length of the side between points W(1, 4) and X(5, -1):

Using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
where \((x_1, y_1) = (1, 4)\) and \((x_2, y_2) = (5, -1)\).

Calculating:
\[
d = \sqrt{(5 - 1)^2 + (-1 - 4)^2}
\]
\[
= \sqrt{(4)^2 + (-5)^2}
\]
\[
= \sqrt{16 + 25}
\]
\[
= \sqrt{41}
\]

Now we calculate the approximate value of \(\sqrt{41}\). Since \(6^2 = 36\) and \(7^2 = 49\), we know that \(\sqrt{41}\) is between 6 and 7. A closer estimation would be about 6.4 units.

The perimeter of the square is given by:
\[
\text{Perimeter} = 4 \times \text{side length} = 4 \times \sqrt{41} \approx 4 \times 6.4 \approx 25.6 \text{ units}
\]

Thus, the measure closest to the perimeter of square WXYZ is:
**25.6 units**.