Question

Find the perimeter of rectangle EFGH , with vertices E(−3,9) , F(1,9) , G(1,−5) , and H(−3,−5) .(1 point)

Answer 1

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

The coordinates of the vertices are:
- \( E(-3, 9) \)
- \( F(1, 9) \)
- \( G(1, -5) \)
- \( H(-3, -5) \)

**Step 1: Calculate the length of side EF.**
The vertices E and F have the same y-coordinate, so we can find the distance (length) between them by subtracting their x-coordinates:

\[
\text{Length of EF} = |x_F - x_E| = |1 - (-3)| = |1 + 3| = 4
\]

**Step 2: Calculate the length of side EH.**
The vertices E and H have the same x-coordinate, so we can find the distance (height) between them by subtracting their y-coordinates:

\[
\text{Length of EH} = |y_E - y_H| = |9 - (-5)| = |9 + 5| = 14
\]

**Step 3: Calculate the perimeter of rectangle EFGH.**
The perimeter \( P \) of a rectangle is given by the formula:

\[
P = 2 \times (\text{Length} + \text{Width}) = 2 \times (\text{EF} + \text{EH})
\]

Substituting the values we found:

\[
P = 2 \times (4 + 14) = 2 \times 18 = 36
\]

Thus, the perimeter of rectangle EFGH is \( \boxed{36} \).