Question

Find the area of rectangle ABCD which has the following vertices:
A(-7,3), B(-2,3), C(-7,-6), D(-2,-6)(1 point)
Responses

10 square units
10 square units

18 square units
18 square units

28 square units
28 square units

45 square units

Answer 1

To find the area of rectangle ABCD given its vertices, we can calculate the lengths of two adjacent sides.

1. **Calculate the length of side AB:**
- Points A and B are given as A(-7, 3) and B(-2, 3).
- Since both points have the same y-coordinate, the length of side AB can be calculated using the difference in x-coordinates:
\[
\text{Length of AB} = |x_B - x_A| = |-2 - (-7)| = |-2 + 7| = |5| = 5 \text{ units}
\]

2. **Calculate the length of side AD:**
- Points A and D are given as A(-7, 3) and D(-2, -6).
- Since both points have the same x-coordinate (x coordinate of point D is actually incorrect, it should be -7 for point A and -2 for point D, both vertical sides).
- The length of side AD can be calculated using the difference in y-coordinates:
\[
\text{Length of AD} = |y_A - y_D| = |3 - (-6)| = |3 + 6| = |9| = 9 \text{ units}
\]

3. **Calculate the area of rectangle ABCD:**
\[
\text{Area} = \text{Length of AB} \times \text{Length of AD} = 5 \times 9 = 45 \text{ square units}
\]

Therefore, the area of rectangle ABCD is **45 square units**.