Question

the vertices of a rectangle are located at (-7, -2) (-3, -2) (-7, -5) (-3, -5) find the perimeter of the rectangle

Answer 1

To find the perimeter of a rectangle, we first need to determine the lengths of its sides. The vertices of the rectangle are given as:

- \( A(-7, -2) \)
- \( B(-3, -2) \)
- \( C(-3, -5) \)
- \( D(-7, -5) \)

### Step 1: Calculate the Lengths of the Sides

1. **Length of Side AB**
\[
AB = |x_2 - x_1| = |-3 - (-7)| = |-3 + 7| = |4| = 4
\]

2. **Length of Side AD (or BC)**
\[
AD = |y_2 - y_1| = |-5 - (-2)| = |-5 + 2| = |-3| = 3
\]

### Step 2: Calculate the Perimeter
The perimeter \( P \) of a rectangle can be calculated using the formula:
\[
P = 2 \times ( \text{Length} + \text{Width} )
\]

Here, the Length is \( AB = 4 \) and the Width is \( AD = 3 \).

\[
P = 2 \times (4 + 3) = 2 \times 7 = 14
\]

### Final Answer
The perimeter of the rectangle is \( \boxed{14} \).