Find the area of rectangle ABCD

Question

that has vertices point A (2,−5)
, point B (5,−5)
, point C (5,−1)
, and point D (2,−1)
in square miles.(1 point)
The area of rectangle ABCD
is
square miles.

Answer 1

To find the area of rectangle ABCD, we first need to determine the lengths of its sides.

1. Calculate the length of side AB:

   • Points A and B are given as A(2, -5) and B(5, -5). Since both points have the same y-coordinate, the distance between them can be calculated using the x-coordinates: \[ \text{Length of AB} = x_B - x_A = 5 - 2 = 3 \text{ miles} \]

2. Calculate the length of side AD:

   • Points A and D are given as A(2, -5) and D(2, -1). Since both points have the same x-coordinate, the distance between them can be calculated using the y-coordinates: \[ \text{Length of AD} = y_D - y_A = -1 - (-5) = -1 + 5 = 4 \text{ miles} \]

3. Calculate the area of rectangle ABCD: The area \( A \) of a rectangle is given by the product of the lengths of its sides: \[ A = \text{Length of AB} \times \text{Length of AD} = 3 \times 4 = 12 \text{ square miles} \]

Thus, the area of rectangle ABCD is \( \boxed{12} \) square miles.