Question

Determine the coordinates of rectangle ABCD. Use the coordinates to compute the area of the rectangle.
Point A: (-3, -2)
Point B: (4, -2)
Point C: (4, 1)
Point D: (-3, 1)

Answer 1

To determine the coordinates of rectangle ABCD, we have:

- Point A: \((-3, -2)\)
- Point B: \((4, -2)\)
- Point C: \((4, 1)\)
- Point D: \((-3, 1)\)

Next, we can verify the shape is a rectangle and calculate its area.

1. **Calculate the lengths of the sides**:
- Length of side \(AB\) (horizontal side) can be calculated as:
\[
AB = x_B - x_A = 4 - (-3) = 4 + 3 = 7
\]

- Length of side \(AD\) (vertical side) can be calculated as:
\[
AD = y_D - y_A = 1 - (-2) = 1 + 2 = 3
\]

2. **Calculate the area of the rectangle**:
The area \(A\) of the rectangle can be calculated using the formula:
\[
A = \text{length} \times \text{width} = AB \times AD
\]
Substituting in the values we found:
\[
A = 7 \times 3 = 21
\]

The coordinates of rectangle ABCD are confirmed, and the area of the rectangle is \(21\) square units.