Answer: The quadrilateral HIJK is a parallelogram.
Explanation:
It is given that the coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).
The parallelogram diagonal theorem states that the quadrilateral is a parallelogram if both diagonal bisects each other.
If HIJK is a quadrilateral, then HJ and IK are the diagonals of HIJK.
First we find the midpoint of HJ.
Now, find the midpoint of IK.
The midpoint of both diagonal are same. It means the diagonals of HIJK bisects each other.
By parallelogram diagonal theorem, we can say that the quadrilateral HIJK is a parallelogram.
