The vertices of square rstv have coordinates r(-1,5), s(-3,1), t(-7,3), and v(-5,7). what is the perimeter of rstv?

The distance between two points (x₁,y₁),(x₂,y₂) = √[(x₂-x₁)² + (y₂-y₁)²]

let the length of the square RSTV = d
So, the perimeter of RSTV = 4 d
d is the distance RS or ST or TV or VR

RS distance between R,S
ST distance between S,T
TV distance between T,V
VR distance between V,R

R(-1,5), S(-3,1), T(-7,3), and V(-5,7)

RS = S - R = √[(-3 - -1)² + (1- 5)²] = √[(-2)² +(-4)² ]= √(4+16) = √20 ≈ 4.472

∴ The perimeter of RSTV = 4 d = 4 * 4.472 = 17.888

The attached figure represents an explanation of the problem.
we should note that:
                                 RS = ST = TV = VR = d ≈ 4.472