Question

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

For points $H(-2,2)$ and $J(4,-2)$, $x=\frac{-2 + 4}{2}=\frac{2}{2}=1$ and $y=\frac{2+( - 2)}{2}=\frac{0}{2}=0$. So the mid - point of $HJ$ is $(1,0)$.

Step3: Find mid - point of diagonal $IK$

For points $I(4,3)$ and $K(-2,-3)$, $x=\frac{4+( - 2)}{2}=\frac{2}{2}=1$ and $y=\frac{3+( - 3)}{2}=\frac{0}{2}=0$. So the mid - point of $IK$ is $(1,0)$.

Answer:

$(1,0)$