Question

hijk is a parallelogram because the midpoint of both diagonals is ____________, which means the diagonals bisect each other. (1, - 1) (1,1) (1,0) (0,1)

Explanation:

Step1: Find the midpoint of diagonal \( HJ \)

The midpoint formula is \( (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) \). For \( H(-2,2) \) and \( J(4,-2) \),
\( x=\frac{-2 + 4}{2}=\frac{2}{2}=1 \)
\( y=\frac{2+( - 2)}{2}=\frac{0}{2}=0 \)

Step2: Find the midpoint of diagonal \( IK \)

For \( I(4,3) \) and \( K(-2,-3) \),
\( x=\frac{4+( - 2)}{2}=\frac{2}{2}=1 \)
\( y=\frac{3+( - 3)}{2}=\frac{0}{2}=0 \)

Answer:

\((1,0)\)