Question

Suppose a parallelogram is drawn on a coordinate plane. Using verticies with coordinates (2,3), (6,3), (7,7), and (3,7) , compute the perimeter. Round your answer to the nearest tenth. (1 point)
The perimeter is approximately
units.

Answer 1

To compute the perimeter of the parallelogram given the vertices \((2,3)\), \((6,3)\), \((7,7)\), and \((3,7)\), we'll first find the lengths of the sides of the parallelogram.

### Step 1: Calculate the lengths of the sides.

1. **Between points \( (2,3) \) and \( (6,3) \)**:
\[
\text{Length} = |x_2 - x_1| = |6 - 2| = 4
\]

2. **Between points \( (6,3) \) and \( (7,7) \)**:
\[
\text{Length} = \sqrt{(7 - 6)^2 + (7 - 3)^2} = \sqrt{1^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17}
\]

3. **Between points \( (7,7) \) and \( (3,7) \)**:
\[
\text{Length} = |x_2 - x_1| = |7 - 3| = 4
\]

4. **Between points \( (3,7) \) and \( (2,3) \)**:
\[
\text{Length} = \sqrt{(2 - 3)^2 + (3 - 7)^2} = \sqrt{(-1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17}
\]

### Step 2: Compute the perimeter.
The perimeter \(P\) of a parallelogram is given by the formula:
\[
P = 2(a + b)
\]
where \(a\) and \(b\) are the lengths of adjacent sides. Here, both lengths \(a\) and \(b\) are \(4\) and \(\sqrt{17}\) respectively.

Calculating the perimeter:
\[
P = 2(4 + \sqrt{17})
\]

### Step 3: Calculate \(\sqrt{17}\).
Using a calculator,
\[
\sqrt{17} \approx 4.123
\]

So now,
\[
P \approx 2(4 + 4.123) = 2 \times 8.123 \approx 16.246
\]

### Final Step: Round the answer.
Rounding to the nearest tenth:
\[
\text{Perimeter} \approx 16.2 \text{ units.}
\]

Thus, the perimeter is approximately **16.2 units**.