Question

Find the area of rectangle ABCD that has vertices point A (−2, −5) , point B (5, −5) , point C (5, −4) , and point D (−2, −4) in square kilometers.(1 point) Responses 16 kilometers 16 kilometers 7 kilometers 7 kilometers 7 square kilometers 7 square kilometers −7 square kilometers

Answer 1

To find the area of rectangle ABCD, we first need to determine the lengths of its sides by calculating the distances between vertices.

Let's find the length of side AB and side AD:

1. **Length of AB**:
- Coordinates of A: \((-2, -5)\)
- Coordinates of B: \((5, -5)\)
- Length of AB = \( x_B - x_A = 5 - (-2) = 5 + 2 = 7 \) kilometers.

2. **Length of AD**:
- Coordinates of A: \((-2, -5)\)
- Coordinates of D: \((-2, -4)\)
- Length of AD = \( y_D - y_A = -4 - (-5) = -4 + 5 = 1 \) kilometer.

Now, we can find the area \( A \) of rectangle ABCD using the formula for the area of a rectangle:
\[
A = \text{length} \times \text{width}
\]
Here:
- Length = \( AB = 7 \) kilometers,
- Width = \( AD = 1 \) kilometer.

Thus, the area is:
\[
A = 7 \text{ km} \times 1 \text{ km} = 7 \text{ square kilometers}.
\]

The area of rectangle ABCD is \( \mathbf{7 \text{ square kilometers}} \).