The points F(8,1) G(2,1), H(−2,−8), and I(4,−8) form parallelogram FGHI. Plot the points then click the "Graph Quadrilateral" button. Then find the perimeter of the parallelogram. Round your answer to the nearest tenth if necessary.

Let's start by plotting the points \( F(8, 1) \), \( G(2, 1) \), \( H(-2, -8) \), and \( I(4, -8) \) to form the parallelogram \( FGHI \). After plotting, we'll calculate the perimeter of the parallelogram.

### Step 1: Plot the Points
- **F** = (8, 1)
- **G** = (2, 1)
- **H** = (-2, -8)
- **I** = (4, -8)

### Step 2: Verify the Parallelogram
For \( FGHI \) to be a parallelogram, opposite sides must be parallel and equal in length. We can confirm this by checking the slopes and lengths of the sides \( FG \), \( GH \), \( HI \), and \( IF \).

### Step 3: Calculate the Length of the Sides
1. **Length of \( FG \)**:
   \[
   FG = \sqrt{(8 - 2)^2 + (1 - 1)^2} = \sqrt{6^2 + 0^2} = \sqrt{36} = 6
   \]

2. **Length of \( GH \)**:
   \[
   GH = \sqrt{(2 - (-2))^2 + (1 - (-8))^2} = \sqrt{4^2 + 9^2} = \sqrt{16 + 81} = \sqrt{97} \approx 9.8
   \]

3. **Length of \( HI \)**:
   \[
   HI = \sqrt{(4 - (-2))^2 + (-8 - (-8))^2} = \sqrt{6^2 + 0^2} = \sqrt{36} = 6
   \]

4. **Length of \( IF \)**:
   \[
   IF = \sqrt{(4 - 8)^2 + (-8 - 1)^2} = \sqrt{(-4)^2 + (-9)^2} = \sqrt{16 + 81} = \sqrt{97} \approx 9.8
   \]

### Step 4: Calculate the Perimeter
The perimeter \( P \) of parallelogram \( FGHI \) is given by the sum of the lengths of all its sides:
\[
P = FG + GH + HI + IF = 6 + 9.8 + 6 + 9.8 = 31.6
\]

### Final Answer
The perimeter of the parallelogram is **31.6 units**.

Would you like further details or have any questions?

### Relative Questions:
1. How do you determine if four points form a parallelogram?
2. Can you explain how to find the midpoint of a line segment?
3. What is the significance of the slope in determining parallel lines?
4. How would you calculate the area of this parallelogram?
5. What are the properties of a parallelogram regarding diagonals?

### Tip:
Always double-check the slopes of opposite sides to ensure they are equal when verifying if a quadrilateral is a parallelogram.

Learn how to calculate the perimeter of parallelogram FGHI with step-by-step instructions and the distance formula. This problem involves plotting points, verifying parallelogram properties, and calculating distances. Suitable for high school students.

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