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 \( \boxed{14} \).