Question

Determine the coordinates of rectangle ABCD . Use the coordinates to compute the area of the rectangle. The coordinates of each point on the graph, are,
D: (-3, 1)
C: (4, 1)
A: (-3, -2)
B: (4, -2).

Answer 1

To determine the coordinates of rectangle ABCD, we first recap the given coordinates of the points:

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

These points represent the vertices of the rectangle. We can visualize the points as follows:

- Points D and C share the same y-coordinate (1) and are horizontally aligned, meaning they form the top side of the rectangle.
- Points A and B share the same y-coordinate (-2) and are horizontally aligned, forming the bottom side of the rectangle.

To find the area of the rectangle, we will first calculate the lengths of its sides (width and height):

1. **Width (length of top or bottom side):**
The distance between points D and C or points A and B will give us the width.
\[
\text{Width} = x_C - x_D = 4 - (-3) = 4 + 3 = 7
\]

2. **Height (length of left or right side):**
The distance between points D and A (or points C and B) will give us the height.
\[
\text{Height} = y_D - y_A = 1 - (-2) = 1 + 2 = 3
\]

3. **Area of Rectangle:**
The area \( A \) of the rectangle can now be computed using the formula:
\[
A = \text{Width} \times \text{Height}
\]
Substituting the values we found:
\[
A = 7 \times 3 = 21
\]

Thus, the coordinates of rectangle ABCD have been determined, and the area of the rectangle is \( \boxed{21} \).