Question

Find the perimeter of rectangle ABCD , with vertices A(−8,3) , B(−1,3) , C(−1,−6) , and D(−8,−6) .(1 point) Responses 36 units 36 units 30 units 30 units 63 units 63 units 32 units

Answer 1

To find the perimeter of rectangle ABCD with vertices A(-8, 3), B(-1, 3), C(-1, -6), and D(-8, -6), we need to first calculate the lengths of the sides.

1. **Calculate the length of AB:**
Points A and B have the same y-coordinate (3). Thus, the length of side AB can be calculated as the difference in x-coordinates:

\[
AB = |x_B - x_A| = |-1 - (-8)| = |-1 + 8| = |7| = 7 \text{ units}
\]

2. **Calculate the length of AD:**
Points A and D have the same x-coordinate (-8). Thus, the length of side AD can be calculated as the difference in y-coordinates:

\[
AD = |y_D - y_A| = |-6 - 3| = |-9| = 9 \text{ units}
\]

3. **The perimeter (P) of the rectangle is given by the formula:**
\[
P = 2 \times (AB + AD)
\]
Substituting the lengths we calculated:
\[
P = 2 \times (7 + 9) = 2 \times 16 = 32 \text{ units}
\]

Therefore, the perimeter of rectangle ABCD is **32 units**.