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The statement that proves that that quadrilateral JKLM is a kite is: (Option B) which indicates that:
LM = MJ = 3; a
JK = KL = √17
We know the following:
J = (4,5)
K = (5,1)
L = (1,2)
M = (1, 5)
We must commence by computing the length of the sides of the quadrilateral using:
D = [tex]\sqrt{((x1-x2)^{2} + (y1 -y2)^{2} }[/tex]
JK = [tex]\sqrt{(4-5)^{2} + (5-1)^{2} }[/tex]
= [tex]\sqrt{17}[/tex]
KL = [tex]\sqrt{(5-1)^{2} + (1-2)^{2} }[/tex]
= [tex]\sqrt{17}[/tex]
LM = [tex]\sqrt{(1-1)^{2} + (5-5)^{2} }[/tex]
= [tex]\sqrt{9}[/tex]
= 3
MJ = [tex]\sqrt{(1-4)^{2} + (5-5)^{2} }[/tex]
= [tex]\sqrt{9}[/tex]
= 3
From the above, it is clear that
LM = MJ = 3; and
JK = KL = [tex]\sqrt{17}[/tex]
QED
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