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)

6.8 units

9.7 units

9.4 units

8.5 units

Answer 1

To find the perimeter of the parallelogram given the vertices \((2,1)\), \((2,3)\), \((4,4)\), and \((4,2)\), we first need to identify the lengths of the sides of the parallelogram.

1. **Identify the vertices**: Let's label the vertices as follows:
- \(A(2, 1)\)
- \(B(2, 3)\)
- \(C(4, 4)\)
- \(D(4, 2)\)

2. **Calculate the lengths of the sides**:
- The distance between points \(A\) and \(B\):
\[
AB = \sqrt{(2 - 2)^2 + (3 - 1)^2} = \sqrt{0 + 2^2} = \sqrt{4} = 2
\]
- The distance between points \(B\) and \(C\):
\[
BC = \sqrt{(4 - 2)^2 + (4 - 3)^2} = \sqrt{2^2 + 1^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236
\]
- The distance between points \(C\) and \(D\):
\[
CD = \sqrt{(4 - 4)^2 + (4 - 2)^2} = \sqrt{0 + 2^2} = \sqrt{4} = 2
\]
- The distance between points \(D\) and \(A\):
\[
DA = \sqrt{(2 - 4)^2 + (1 - 2)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236
\]

3. **Calculate the perimeter**:
The perimeter \(P\) of the parallelogram is given by adding the lengths of all sides:
\[
P = AB + BC + CD + DA = 2 + 2.236 + 2 + 2.236 \approx 8.472
\]

4. **Round the perimeter to the nearest tenth**:
\[
P \approx 8.5 \text{ units}
\]

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