Question

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

Answer 1

Let's start by evaluating the coordinates of the points A, B, C, and D.

- A = (-3, -2)
- B = (4, -2)
- C = (4, 1)
- D = (-3, 1)

### Step 1: Visualizing the Rectangle
We can visualize these points on a coordinate plane:

- Point A is located at (-3, -2).
- Point B is located at (4, -2).
- Point C is located at (4, 1).
- Point D is located at (-3, 1).

### Step 2: Determine the dimensions (length and width)
The rectangle can be analyzed by determining the lengths of its sides.

1. **Length of AB (width of the rectangle)**:
Since A and B have the same y-coordinate (-2), we find the length between points A and B using the x-coordinates:
\[
AB = x_B - x_A = 4 - (-3) = 4 + 3 = 7.
\]

2. **Length of AD (height of the rectangle)**:
Since A and D have the same x-coordinate (-3), we find the length between points A and D using the y-coordinates:
\[
AD = y_D - y_A = 1 - (-2) = 1 + 2 = 3.
\]

### Step 3: Calculate the area of rectangle ABCD
Now, we can find the area of the rectangle using the formula for the area \( A \) of a rectangle:
\[
A = \text{length} \times \text{width} = AB \times AD.
\]
Substituting the values we found:
\[
A = 7 \times 3 = 21.
\]

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