Answer:
[tex]4\sqrt{37} units[/tex] is the perimeter of square ABCD.
Step-by-step explanation:
Coordinates of square ABCD:
A = (3,4), B = (2,-2), C = (-4-1) , D = (-3,5)
Distance formula: [tex](x_1,y_1),(x_2,y_2)[/tex]
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance of AB: A = (3,4), B = (2,-2)
[tex]AB=\sqrt{(2-3)^2+(-2-4)^2}[/tex]
[tex]AB=\sqrt{(-1)^2+(-6)^2}=\sqrt{37} units[/tex]
Given that the ABCD is square, then:
AB = BC = CD = DA
Perimeter of the square ABC = AB +BC + CD + DA
[tex] AB+ AB+ AB+ AB= 4AB=4\sqrt{37} units[/tex]
[tex]4\sqrt{37} units[/tex] is the perimeter of square ABCD.
