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: 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 $J(4,-2)$, $x=\frac{-2 + 4}{2}=\frac{2}{2}=1$, $y=\frac{2+( - 2)}{2}=\frac{2 - 2}{2}=0$.

Step3: Find mid - point of diagonal IK (optional verification)

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

Answer:

C. $(1,0)$