Question

What’s the area of a rectangle with points ABCD on a coordinate plane in square miles if A is 2, -5, B is 5, -5, C is 5,-1 and point D being 2,-1

Answer 1

To find the area of the rectangle defined by the points A(2, -5), B(5, -5), C(5, -1), and D(2, -1) on the coordinate plane, we first need to determine the lengths of the sides of the rectangle.

1. **Identify the coordinates:**
- A(2, -5)
- B(5, -5)
- C(5, -1)
- D(2, -1)

2. **Length of the sides:**
- The length of side AB (horizontal side) can be calculated as the distance between points A and B:
\[
\text{Length of AB} = |x_B - x_A| = |5 - 2| = 3
\]

- The length of side AD (vertical side) can be calculated as the distance between points A and D:
\[
\text{Length of AD} = |y_D - y_A| = |-1 - (-5)| = |-1 + 5| = 4
\]

3. **Calculating the area:**
The area \(A\) of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width}
\]
Substituting the lengths we calculated:
\[
A = 3 \times 4 = 12
\]

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