Question

Use the coordinates to compute the perimeter of a paralleleogram whose vertices are located at the ordered pairs (0, 0), (1, 2), (2, 1) and (1, -1).
A. 7.2 units
B. 4 units

Answer 1

To calculate the perimeter of the parallelogram with given vertices, we can follow these steps:

1. **Identify the vertices**:
- A = (0, 0)
- B = (1, 2)
- C = (2, 1)
- D = (1, -1)

2. **Calculate the lengths of the sides**:
We will calculate the lengths of AB, BC, CD, and DA.

- **Length of AB**:
\[
AB = \sqrt{(1-0)^2 + (2-0)^2} = \sqrt{1^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5}
\]

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

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

- **Length of DA**:
\[
DA = \sqrt{(1-0)^2 + (-1-0)^2} = \sqrt{1^2 + (-1)^2} = \sqrt{1 + 1} = \sqrt{2}
\]

3. **Sum the lengths to find the perimeter**:
Since opposite sides of a parallelogram are equal, we can calculate the perimeter as follows:
\[
\text{Perimeter} = 2(AB + BC)
\]
Plugging in the values we calculated:
\[
\text{Perimeter} = 2(\sqrt{5} + \sqrt{2})
\]

4. **Numerical approximation**:
We can also calculate the approximate values of \(\sqrt{5}\) and \(\sqrt{2}\):
\[
\sqrt{5} \approx 2.236, \quad \sqrt{2} \approx 1.414
\]
Thus,
\[
\text{Perimeter} \approx 2(2.236 + 1.414) \approx 2(3.650) \approx 7.3
\]

Since the values don't exactly match the options provided but are close to 7.2, the best estimate would be:

**A. 7.2 units**