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)

30 units^2

8 units^2

16 units^2

15 units^2

Answers

Answered by GPT-4o mini
To find the area of the rectangle formed by the points A, B, C, and D, we will first identify the coordinates of the vertices:

- A = (-5, 6)
- B = (-2, 6)
- C = (-2, 1)
- D = (-5, 1)

Next, we can determine the lengths of the sides of the rectangle.

1. **Length of AB** (horizontal side):
Since A and B have the same y-coordinate (y = 6), the length can be computed as:
\[
\text{Length of AB} = x_B - x_A = -2 - (-5) = -2 + 5 = 3 \text{ units}
\]

2. **Length of AD** (vertical side):
Since A and D have the same x-coordinate (x = -5), the length can be computed as:
\[
\text{Length of AD} = y_A - y_D = 6 - 1 = 5 \text{ units}
\]

Now, we can calculate the area of the rectangle using the formula for area:
\[
\text{Area} = \text{Length} \times \text{Width} = \text{Length of AB} \times \text{Length of AD} = 3 \text{ units} \times 5 \text{ units} = 15 \text{ units}^2
\]

Therefore, the area of the rectangle is **15 units²**.
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