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.