Question

Suppose a parallelogram is drawn on a coordinate plane. Using vertices with the coordinates (2, 1), (2, 3), (4, 4), and (4, 2), compute the perimeter. Round your answer to the nearest tenth. (1 point)
The perimeter is approximately units.

Answer 1

To find the perimeter of the parallelogram with vertices at (2, 1), (2, 3), (4, 4), and (4, 2), we first need to determine the lengths of the sides.

1. **Identify the Lengths of the Sides:**
- Side between (2, 1) and (2, 3):
\[
\text{Length} = \sqrt{(2 - 2)^2 + (3 - 1)^2} = \sqrt{0 + 2^2} = \sqrt{4} = 2
\]

- Side between (2, 3) and (4, 4):
\[
\text{Length} = \sqrt{(4 - 2)^2 + (4 - 3)^2} = \sqrt{2^2 + 1^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236
\]

- Side between (4, 4) and (4, 2):
\[
\text{Length} = \sqrt{(4 - 4)^2 + (2 - 4)^2} = \sqrt{0 + (-2)^2} = \sqrt{4} = 2
\]

- Side between (4, 2) and (2, 1):
\[
\text{Length} = \sqrt{(2 - 4)^2 + (1 - 2)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236
\]

2. **Calculate the Perimeter:**
The perimeter \( P \) of the parallelogram is given by the sum of the lengths of all sides:
\[
P = 2 + 2.236 + 2 + 2.236 = 8.472
\]

3. **Round to the Nearest Tenth:**
\[
P \approx 8.5
\]

Thus, the perimeter of the parallelogram is approximately 8.5 units.