Question

Which statement proves that quadrilateral HIJK is a kite? HI ⊥ IJ, and m∠H = m∠J. IH = IJ = 3 and JK = HK = StartRoot 29 EndRoot, and IH ≠ JK and IJ ≠ HK. IK intersects HJ at the midpoint of HJ at (−1. 5, 2. 5). The slope of HK = Negative two-fifths and the slope of JK = Negative five-halves.

Answer 1

Answer:

B.

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

Answer 2

The statement proves that quadrilateral HIJK is a kite is  IH = IJ = 3 and JK = HK = $\sqrt{29}$ and IH ≠ JK and IJ ≠ HK.

Given

On a coordinate plane, kite H I J K with diagonals is shown.

Point H is at (negative 3, 1), the point I is at (negative 3, 4), point J is at (0, 4), and point K is at (2, negative 1).

What is the kite?

A quadrilateral is called a kite with two pairs of equal adjacent sides but unequal opposite sides.

Firstly calculating the length of the sides of the kite using the following formula;

$\rm Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

For a kite quadrilateral,  HIJK will be a kite, if it's siding IJ = IH

From the graph length of I H = 4 - 1 = 3 units

Length of IJ = 0 - (-3) = 3 units

Therefore, IJ = IH = 3 units

Sides HK should be equal to JK

Length of HK is;

$\rm HK =\sqrt{(1-(-1))^2+(2-(-3))^2} \\\\HK=\sqrt{(1+1)^2+(2+3)^2} \\\\HK=\sqrt{(2)^2+(5)^2\\} \\\\ HK =\sqrt{4+25} \\\\HK= \sqrt{29}$

Hence, the statement proves that quadrilateral HIJK is a kite is  IH = IJ = 3 and JK = HK = $\sqrt{29}$ and IH ≠ JK and IJ ≠ HK.

To know more about quadrilateral click the link given below.

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