Question

Find the coordinates of the rectangle and use them to compute the area.
Point A: (-5, 6)
Point B: (-2, 6)
Point C: (-2, 1)
Point D: (-5, 1)
A: 8 units^2
B. 15 units^2
C. 30 units^2
D. 16 units^2

Answer 1

To find the area of the rectangle formed by the points A, B, C, and D, we first need to confirm the arrangement of points and then compute the lengths of the sides.

Given:
- Point A: (-5, 6)
- Point B: (-2, 6)
- Point C: (-2, 1)
- Point D: (-5, 1)

From the coordinates:
- Points A and B are on the top horizontal side (both have the same y-coordinate of 6).
- Points C and D are on the bottom horizontal side (both have the same y-coordinate of 1).
- Points A and D are on the left vertical side (both have the same x-coordinate of -5).
- Points B and C are on the right vertical side (both have the same x-coordinate of -2).

Calculating the length of rectangle:
- The length of the rectangle (horizontal sides):
\[
\text{Length} = |x_B - x_A| = |-2 - (-5)| = |-2 + 5| = 3
\]

- The width of the rectangle (vertical sides):
\[
\text{Width} = |y_A - y_D| = |6 - 1| = 5
\]

Now, the area of the rectangle is given by:
\[
\text{Area} = \text{Length} \times \text{Width} = 3 \times 5 = 15 \text{ units}^2
\]

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

The correct answer is **B. 15 units²**.