The statement proves that quadrilateral HIJK is a kite is IH = IJ = 3 and JK = HK = [tex]\sqrt{29}[/tex] 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).
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;
[tex]\rm Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
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;
[tex]\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}[/tex]
Hence, the statement proves that quadrilateral HIJK is a kite is IH = IJ = 3 and JK = HK = [tex]\sqrt{29}[/tex] and IH ≠ JK and IJ ≠ HK.
To know more about quadrilateral click the link given below.
https://brainly.com/question/1751208
Answer:
B.
IH = IJ = 3 and JK = HK = StartRoot 29 EndRoot, and IH ≠ JK and IJ ≠ HK.
