Question

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

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Find mid - point of diagonal $HK$

For points $H(-2,2)$ and $K(-2,-3)$, $x=\frac{-2+( - 2)}{2}=\frac{-4}{2}=-2$, $y=\frac{2+( - 3)}{2}=-\frac{1}{2}$. This is wrong. Let's find mid - point of diagonal $IJ$.

Step3: Find mid - point of diagonal $IJ$

For points $I(4,3)$ and $J(4,-2)$, $x=\frac{4 + 4}{2}=4$, $y=\frac{3+( - 2)}{2}=\frac{1}{2}$. This is wrong. Let's find mid - point of diagonal $HJ$ and $IK$.
For points $H(-2,2)$ and $J(4,-2)$:
$x=\frac{-2 + 4}{2}=\frac{2}{2}=1$
$y=\frac{2+( - 2)}{2}=\frac{0}{2}=0$
For points $I(4,3)$ and $K(-2,-3)$:
$x=\frac{4+( - 2)}{2}=\frac{2}{2}=1$
$y=\frac{3+( - 3)}{2}=\frac{0}{2}=0$

Answer:

C. $(1,0)$