Question

What is the perimeter of rectangle FGHI
F=(-7,8)
G=(1,8)
H=(1,9)
I=(-7,9)
Perimeter = _____ Units

Answer 1

To find the perimeter of rectangle FGHI, we first need to determine the lengths of its sides.

1. **Find the lengths of the sides:**

- The length (width) can be found using points F and G:
- Coordinates of F = (-7, 8)
- Coordinates of G = (1, 8)
- The distance between F and G is calculated using the formula for distance between two points on a line (since they have the same y-coordinate):
\[
\text{Length} = |x_2 - x_1| = |1 - (-7)| = 1 + 7 = 8 \text{ units}
\]

- The height can be found using points G and H:
- Coordinates of G = (1, 8)
- Coordinates of H = (1, 9)
- The distance between G and H is calculated using the formula for distance between two points on a vertical line (since they have the same x-coordinate):
\[
\text{Height} = |y_2 - y_1| = |9 - 8| = 1 \text{ unit}
\]

2. **Calculate the perimeter:**
The formula for the perimeter \( P \) of a rectangle is given by:
\[
P = 2(\text{Length} + \text{Height})
\]
Substituting the values we found:
\[
P = 2(8 + 1) = 2 \times 9 = 18 \text{ units}
\]

Therefore, the perimeter of rectangle FGHI is **18 units**.