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Quadrilateral ABCD has the following vertices.

A(-5, 5) B(4, 5) C(2, 0) D(-5, -2)

Determine the length of the sides of the quadrilateral, and arrange them in order from longest length to shortest length.

Sagot :

darth666
A(-5,5)
B(4,5)
C(2,0)
D(-5,-2)

AB,BC,CD,DA

AB = [4-(-5)),5-5]=[9,0]
Lenght  [tex]AB= \sqrt{9^2+0^2}= \sqrt{81} =9[/tex]

BC = [2-4,0-5]=[-2,-5]
Lenght  [tex]BC=\sqrt{(-2)^2+(-5)^2}=\sqrt{4+25}=\sqrt{29}[/tex]

CD = [-5-2,-2-0]=[-7,-2]
Lenght  [tex]CD=\sqrt{(-7)^2+(-2)^2}=\sqrt{49+4}=\sqrt{53}[/tex]

DA =[-5-(-5),-2-5]=[0,-7]
Lenght [tex]DA=\sqrt{0^2+(-7)^2}=\sqrt{49}=7[/tex]

sorted from longest to shortest:
AB, CD,DA,BC
[tex]\sqrt{81}, \sqrt{53}, \sqrt{49}, \sqrt{29}[/tex]

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