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: Identify diagonal points

Let's consider the diagonals of the parallelogram. Diagonal 1 has endpoints $H(-2,2)$ and $J(4,-2)$.

Step3: Calculate mid - point of diagonal 1

Using the mid - point formula:
$x=\frac{-2 + 4}{2}=\frac{2}{2}=1$
$y=\frac{2+( - 2)}{2}=\frac{2 - 2}{2}=0$
The mid - point of the diagonal with endpoints $H(-2,2)$ and $J(4,-2)$ is $(1,0)$. We can also check with the other diagonal (endpoints $I(4,3)$ 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:

$(1,0)$