Question

Find the coordinates of the rectangle and use them to compute the area.
A(-5,6) B(-2,6) C(-2,1) D(-5,1)

Answer 1

To find the area of the rectangle formed by the points A(-5,6), B(-2,6), C(-2,1), and D(-5,1), we can start by determining the lengths of the sides of the rectangle.

1. **Coordinates of the points**:
- A(-5, 6) is at the top left.
- B(-2, 6) is at the top right.
- C(-2, 1) is at the bottom right.
- D(-5, 1) is at the bottom left.

2. **Lengths of the sides**:
- **Length of AB** (horizontal distance between A and B):
\[
AB = x_B - x_A = -2 - (-5) = -2 + 5 = 3
\]

- **Length of AD** (vertical distance between A and D):
\[
AD = y_A - y_D = 6 - 1 = 5
\]

3. **Area of the rectangle**:
The area \( A \) of a rectangle is given by the formula:
\[
A = \text{Length} \times \text{Width}
\]
Substituting the lengths we found:
\[
A = AB \times AD = 3 \times 5 = 15
\]

Thus, the area of the rectangle is \( 15 \) square units.