Question

Suppose a parallelogram is drawn on a coordinate plane. Using vertices with the coordinates  (0,0) ,  (2,3) ,  (5,2) , and  (3,−1) , compute the perimeter. Round your answer to the nearest tenth.(1 point)The perimeter is approximately  units

Answer 1

To find the perimeter of the parallelogram formed by the vertices (0,0), (2,3), (5,2), and (3,-1), we first need to calculate the lengths of the sides.

The perimeter of a parallelogram is given by the formula:

\[
P = 2 \times (a + b)
\]

where \(a\) and \(b\) are the lengths of the adjacent sides.

**Step 1: Calculate the distances between adjacent vertices.**

1. Distance between (0, 0) and (2, 3):
\[
d_1 = \sqrt{(2-0)^2 + (3-0)^2} = \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13} \approx 3.6
\]

2. Distance between (2, 3) and (5, 2):
\[
d_2 = \sqrt{(5-2)^2 + (2-3)^2} = \sqrt{3^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10} \approx 3.2
\]

3. Distance between (5, 2) and (3, -1):
\[
d_3 = \sqrt{(3-5)^2 + (-1-2)^2} = \sqrt{(-2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13} \approx 3.6
\]

4. Distance between (3, -1) and (0, 0):
\[
d_4 = \sqrt{(0-3)^2 + (0-(-1))^2} = \sqrt{(-3)^2 + (1)^2} = \sqrt{9 + 1} = \sqrt{10} \approx 3.2
\]

**Step 2: Add the lengths of two adjacent sides.**

From the calculations above:
- One side length is \( \sqrt{13} \approx 3.6 \).
- The other side length is \( \sqrt{10} \approx 3.2 \).

**Step 3: Calculate the perimeter.**

Using the lengths:
\[
P \approx 2 \times (3.6 + 3.2) \approx 2 \times 6.8 = 13.6
\]

Therefore, the perimeter of the parallelogram is approximately **13.6 units**.