Answer:
Option B. is the answer.
Step-by-step explanation:
In the given picture we have to prove that quadrilateral HIJK is a kite.
1. For a kite quadrilateral HIJK will be a kite, if it's sides 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
2. Sides HK should be equal to JK
Length of HK = [tex]\sqrt{[1-(-1)]^{2}+[2-(-3)^{2}[/tex] by Pythagoras Theorem
= [tex]\sqrt{(2)^{2}+(5)^{2}}=\sqrt{4+25}=\sqrt{29}[/tex]
Similarly length of JK = [tex]\sqrt{(2)^{2}+[4-(-1)]^{2}}=\sqrt{4+5^{2} }[/tex]
= [tex]\sqrt{29}[/tex]
Therefore HK = JK = √29 units
3). IH ≠ JK and ij ≠ HK
All these conditions are fulfilled for HIJK to be a kite.
Option B. is the answer.
