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)
Responses

8.5 units
8.5 units

9.4 units
9.4 units

9.7 units
9.7 units

6.8 units

Answer 1

To find the perimeter of the parallelogram defined by the vertices (2,1), (2,3), (4,4), and (4,2), we first need to calculate the lengths of the sides.

Let's identify the sides of the parallelogram based on these points. We can organize the points in order.

1. Vertex A: (2,1)
2. Vertex B: (2,3)
3. Vertex C: (4,4)
4. Vertex D: (4,2)

Now we can find the length of each side:

1. **Length of AB**:
\[
AB = \sqrt{(2 - 2)^2 + (3 - 1)^2} = \sqrt{0 + 4} = \sqrt{4} = 2 \text{ units}
\]

2. **Length of BC**:
\[
BC = \sqrt{(4 - 2)^2 + (4 - 3)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236 \text{ units}
\]

3. **Length of CD**:
\[
CD = \sqrt{(4 - 4)^2 + (2 - 4)^2} = \sqrt{0 + 4} = \sqrt{4} = 2 \text{ units}
\]

4. **Length of DA**:
\[
DA = \sqrt{(2 - 4)^2 + (1 - 2)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236 \text{ units}
\]

Now we compute the perimeter \( P \) of the parallelogram by adding the lengths of all the sides:

\[
P = AB + BC + CD + DA = 2 + 2.236 + 2 + 2.236 = 8.472 \text{ units}
\]

Rounding to the nearest tenth, the perimeter is approximately:

\[
\boxed{8.5} \text{ units}
\]