Question

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.

Answer 1

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

AB,BC,CD,DA

AB = [4-(-5)),5-5]=[9,0]
Lenght
`AB= √(9^2+0^2)= √(81) =9`

BC = [2-4,0-5]=[-2,-5]
Lenght
`BC=√((-2)^2+(-5)^2)=√(4+25)=√(29)`

CD = [-5-2,-2-0]=[-7,-2]
Lenght
`CD=√((-7)^2+(-2)^2)=√(49+4)=√(53)`

DA =[-5-(-5),-2-5]=[0,-7]
Lenght
`DA=√(0^2+(-7)^2)=√(49)=7`

sorted from longest to shortest:
AB, CD,DA,BC

`√(81), √(53), √(49), √(29)`