Question

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

Answer 1

so its 9.4?

Answer 2

so its 9.4? yes or no

Answer 3

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

1. **Identify the vertices**:
- A = (2, 1)
- B = (2, 3)
- C = (4, 4)
- D = (4, 2)

2. **Calculate the lengths of the sides**:
We check two sides: AB and AD.

**Length of AB**:
\[
AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2 - 2)^2 + (3 - 1)^2} = \sqrt{0 + 2^2} = \sqrt{4} = 2
\]

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

**Length of CD** (which is equal to AB since it's opposite):
\[
CD = \sqrt{(4 - 4)^2 + (2 - 4)^2} = \sqrt{0 + (-2)^2} = \sqrt{4} = 2
\]

**Length of DA** (which is equal to BC since it's opposite):
\[
DA = \sqrt{(2 - 4)^2 + (1 - 2)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5}
\]

3. **Compute the perimeter**:
The perimeter \(P\) of the parallelogram can be calculated using:
\[
P = 2(AB + BC) = 2(2 + \sqrt{5})
\]
Approximating \(\sqrt{5} \approx 2.236\), we have:
\[
P \approx 2(2 + 2.236) = 2(4.236) \approx 8.472
\]

4. **Round to the nearest tenth**:
\[
P \approx 8.5
\]

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