https://file.aiquickdraw.com/mathbot/file/17255604308121a4d0zvk.jpg

The problem asks to determine why shape HJKL is a parallelogram, specifically by finding the midpoint of both diagonals, which confirms that the diagonals bisect each other.

### Step 1: Identify the Coordinates
The vertices of the parallelogram are:
- H(-2, 2)
- J(4, 5)
- K(-2, -5)
- L(4, -2)

### Step 2: Find the Midpoint of Diagonals
The midpoints of diagonals are calculated using the midpoint formula:

\[
\text{Midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

#### Midpoint of Diagonal HJ and KL:
1. Diagonal from H to L:
   - Points: H(-2, 2) and L(4, -2)
   - Midpoint: 

     \[
     \left(\frac{-2 + 4}{2}, \frac{2 + (-2)}{2}\right) = \left(1, 0\right)
     \]

2. Diagonal from J to K:
   - Points: J(4, 5) and K(-2, -5)
   - Midpoint: 

     \[
     \left(\frac{4 + (-2)}{2}, \frac{5 + (-5)}{2}\right) = \left(1, 0\right)
     \]

Since both midpoints are \((1, 0)\), the diagonals bisect each other, confirming that HJKL is a parallelogram.

### Answer
The correct option is **C: (1, 0)**.

Would you like further details or have any other questions?

### Related Questions
1. How can you verify if a quadrilateral is a parallelogram using slope?
2. How do you calculate the distance between two points on a coordinate plane?
3. What is the significance of diagonals bisecting each other in a parallelogram?
4. How can the properties of midpoints help determine the types of quadrilaterals?
5. What are the other ways to prove that a quadrilateral is a parallelogram?

### Tip
Always double-check your midpoint calculations to ensure the diagonals' bisecting point is correct, confirming the properties of geometric shapes.

HLJK is a parallelogram because the midpoint of both diagonals is ________, which means the diagonals bisect each other.

Learn how to prove a quadrilateral is a parallelogram by using the midpoint formula in coordinate geometry. The problem involves calculating the midpoints of diagonals to confirm that they bisect each other. Suitable for students in Grades 8-10.

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