Question

What is te perimeter of square FGHI
F=(0,-10)
G=(0,-7)
H=(-7,3)
I=(-10,3)
Perimeter = ______ Units

Answer 1

To find the perimeter of square FGHI, we first need to determine the length of one of its sides.

Let's find the distance between two adjacent vertices, such as F and G. The coordinates of F and G are:
- \( F = (0, -10) \)
- \( G = (0, -7) \)

Using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
we can calculate the distance between F and G:

\[
d = \sqrt{(0 - 0)^2 + (-7 - (-10))^2} = \sqrt{0 + (-7 + 10)^2} = \sqrt{0 + 3^2} = \sqrt{9} = 3
\]

The length of one side of the square is 3 units.

The perimeter \( P \) of a square is given by the formula:
\[
P = 4 \times \text{side length}
\]

Thus, the perimeter of square FGHI is:
\[
P = 4 \times 3 = 12 \text{ units}
\]

Therefore, the perimeter of square FGHI is \( \boxed{12} \) units.