Question

The vertices of a rectangle are located at (-7, -2), (-3, -2), (-7, -5), (-3, -5). Find the perimeter of the rectangle.(1 point) Responses 10 units 10 units 12 units 12 units 14 units 14 units 16 units

Answer 1

To find the perimeter of the rectangle, we first need to determine the lengths of its sides.

The vertices of the rectangle are:
- A(-7, -2)
- B(-3, -2)
- C(-3, -5)
- D(-7, -5)

1. **Calculate the length of the horizontal sides (AB and CD)**:
- The length can be found by taking the difference in the x-coordinates of points A and B (or C and D):
\[
|x_2 - x_1| = |-3 - (-7)| = |-3 + 7| = |4| = 4 \text{ units}
\]

2. **Calculate the length of the vertical sides (AD and BC)**:
- The length can be found by taking the difference in the y-coordinates of points A and D (or B and C):
\[
|y_2 - y_1| = |-5 - (-2)| = |-5 + 2| = |-3| = 3 \text{ units}
\]

3. **Calculate the perimeter of the rectangle**:
- The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times (\text{length} + \text{width})
\]
where length is 4 units and width is 3 units.
\[
P = 2 \times (4 + 3) = 2 \times 7 = 14 \text{ units}
\]

Thus, the perimeter of the rectangle is **14 units**.