Answer:
The perimeter of rhombus WXYZ is [tex]4 \sqrt{13}[/tex]
Step-by-step explanation:
Step 1 :Finding length of XY
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= 5
[tex]x_2[/tex]=3
[tex]y_1[/tex]= -1
[tex]y_2[/tex]=2
XY = [tex]\sqrt{(3-5)^2 +(2 -(-1))^2}[/tex]
XY = [tex]\sqrt{(3-5)^2 +(2 +1))^2}[/tex]
XY = [tex]\sqrt{(-2)^2 +(3))^2}[/tex]
XY = [tex]\sqrt{4 +9}[/tex]
XY = [tex]\sqrt{(13)}[/tex]
Step 2 :Finding length of YZ
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= 3
[tex]x_2[/tex]=5
[tex]y_1[/tex]= 2
[tex]y_2[/tex]=5
YZ = [tex]\sqrt{(5-3)^2 +(5-2)^2}[/tex]
YZ = [tex]\sqrt{(2)^2 +(3)^2}[/tex]
YZ = [tex]\sqrt{4 +9}[/tex]
YZ = [tex]\sqrt{(13)}[/tex]
Step 3 : :Finding length of ZW
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= 5
[tex]x_2[/tex]=7
[tex]y_1[/tex]= 5
[tex]y_2[/tex]=2
ZW = [tex]\sqrt{(7-5)^2 +(5-2)^2}[/tex]
ZW = [tex]\sqrt{(2)^2 +(3)^2}[/tex]
ZW = [tex]\sqrt{4 +9}[/tex]
ZW = [tex]\sqrt{(13)}[/tex]
Step 4 :Finding length of WX
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= 7
[tex]x_2[/tex]=5
[tex]y_1[/tex]= 2
[tex]y_2[/tex]= -1
WX = [tex]\sqrt{(7-5)^2 +((-1)-2)^2}[/tex]
WX = [tex]\sqrt{(2)^2 +(-3)^2}[/tex]
WX = [tex]\sqrt{4 +9}[/tex]
WX = [tex]\sqrt{(13)}[/tex]
Step 5: finding the perimeter of the rhombus
Perimeter= 4 X side
=> [tex]4 \times \sqrt{13}[/tex]
=> [tex]4 \sqrt{13}[/tex]
