Question

On a coordinate plane, quadrilateral J K L M with diagonals is shown. Point J is at (4, 5), point K is at (5, 1), point L is at (1, 2), and point M is at (1, 5). Which statement proves that quadrilateral JKLM is a kite?

Answer 1

Answer:

B)  LM = JM = 3 and JK = LK = $\sqrt{17}$

Step-by-step explanation:

Edge 2021

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Answer 2

Answer:

$LM = MJ = 3$

$JK = KL = \sqrt{17$

Step-by-step explanation:

Given

$J = (4,5)$

$K = (5,1)$

$L = (1,2)$

$M = (1,5)$

Required

Prove it's a kite

Start by calculating the length of the sides of the kite using:

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

$JK = \sqrt{(4 - 5)^2 + (5 -1)^2} = \sqrt{17}$

$KL = \sqrt{(5 - 1)^2 + (1 -2)^2} = \sqrt{17}$

$LM = \sqrt{(1 - 1)^2 + (2 -5)^2} = \sqrt{9} =3$

$MJ = \sqrt{(1 - 4)^2 + (5 -5)^2} =\sqrt{9} = 3$

Hence:

$LM = MJ = 3$

$JK = KL = \sqrt{17$

proves that it is a kite