Question

suppose a parallelogram is drawn on a coordinate plane. using vertices with the coordinates (2,1),(2,3),(4,4),&(4,2) compute the perimeter. round your answer to the nearest tenth

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 find the lengths of its sides.

1. **Calculate 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)**:
\[
\text{Length} = \sqrt{(4 - 2)^2 + (4 - 3)^2} = \sqrt{2^2 + 1^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.2
\]

- **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)**:
\[
\text{Length} = \sqrt{(2 - 4)^2 + (1 - 2)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.2
\]

2. **Sum the lengths of the sides to find the perimeter.** Each pair of opposite sides has the same length:

\[
\text{Perimeter} = 2 + \sqrt{5} + 2 + \sqrt{5} = 4 + 2\sqrt{5}
\]

Using \(\sqrt{5} \approx 2.236\):

\[
2\sqrt{5} \approx 2 \times 2.236 \approx 4.472
\]

Therefore, the perimeter is:

\[
\text{Perimeter} \approx 4 + 4.472 \approx 8.472
\]

3. **Round to the nearest tenth**:

The total perimeter, rounded to the nearest tenth, is approximately:

\[
\text{Perimeter} \approx 8.5
\]

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