Question

D(-3,5)

What is the perimeter of square ABCD?
A(3,4)
+
37 units
cb
4/37 units
28 units
37 units
.
-54-3 -2 -
2
3
4
5
C(-4-1)
B(2,-2)

Answer 1

`4√(37) units` is the perimeter of square ABCD.

Explanation:

Coordinates of square ABCD:

A = (3,4), B = (2,-2), C = (-4-1) , D = (-3,5)

Distance formula:
`(x_1,y_1),(x_2,y_2)`

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Distance of AB: A = (3,4), B = (2,-2)

`AB=√((2-3)^2+(-2-4)^2)`

`AB=√((-1)^2+(-6)^2)=√(37) units`

Given that the ABCD is square, then:

AB = BC = CD = DA

Perimeter of the square ABC = AB +BC + CD + DA

`AB+ AB+ AB+ AB= 4AB=4√(37) units`

`4√(37) units` is the perimeter of square ABCD.