Question

What is the perimeter of square UVWX?
U = (-5, 6)
V = (10,6)
W = (10,-9)
X = (-5,-9)
Perimeter= ____units

Answer 1

To find the perimeter of square UVWX, we first need to determine the length of one side of the square. We can do this by calculating the distance between two adjacent vertices of the square, for example, points U and V.

The coordinates of the points are:
- \( U = (-5, 6) \)
- \( V = (10, 6) \)

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Calculating the distance between U and V:
\[
d = \sqrt{(10 - (-5))^2 + (6 - 6)^2} = \sqrt{(10 + 5)^2 + 0^2} = \sqrt{15^2} = 15
\]

Now that we have the length of one side (which is 15 units), we can calculate the perimeter \( P \) of the square using the formula:
\[
P = 4 \times \text{side length}
\]
\[
P = 4 \times 15 = 60 \text{ units}
\]

Thus, the perimeter of square UVWX is:
\[
\text{Perimeter} = 60 \text{ units}
\]