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Studentka2010 [4]
3 years ago
10

The coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).

Mathematics
2 answers:
zhuklara [117]3 years ago
8 0

Answer: IH = IJ = 3 and JK = HK = StartRoot 29 EndRoot, and IH ≠ JK and IJ ≠ HK.

Step-by-step explanation:

pogonyaev3 years ago
7 0

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.

\text{Midpoint of HJ}=(\frac{0+4}{2}, \frac{5-1}{2})

\text{Midpoint of HJ}=(2,2)

Now, find the midpoint of IK.

\text{Midpoint of IK}=(\frac{3+1}{2}, \frac{3+1}{2})

\text{Midpoint of IK}=(2,2)

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.

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