Find the perimeter of the polygon with x (-1,3), y (3,0), z (-1,-2)

The distance formula (actually, the Pythagorean Theorem) that gives the distance between the points  (x₁, y₁)  and  (x₂, y₂)    is:  d  =  √[ (x₂ - x_{1)² +} (y₂ - y₁)² ]

The distance from  x(-1, 3)  and  y(3,0):

call  x₁ = -1,  y₁ = 3,  x₂ = 3,  y₂ = 0:  

       d  =   √[ (3 - -1)_² + (0 - 3)² ]  =  √[ (4)_² + (- 3)² ]  =  √[ 16 + 9 ]  =  √[ 25 ]  =  5

The distance from  y(3,0)  and  z(-1,-2):

call  x₁ = 3,  y₁ = 0,  x₂ = -1,  y₂ = -2:  

       d  =   √[ (-1 - 3)_² + (-2 - 0)² ]  =  √[ (-4)_² + (- 2)² ]  =  √[ 16 + 4 ]  =  √[ 20 ]                  =  2√5

The distance from  x(-1, 3)  and  z(-1,-2):

call  x₁ = -1,  y₁ = 3,  x₂ = -1,  y₂ = -2:  

       d  =   √[ (-1 - -1)_² + (-2 - 3)² ]  =  √[ (0)_² + (- 5)² ]  =  √[ 0 + 5 ]  =  √[ 25 ]  =  5

The total distance will be  5 + 2√5 + 5  =  10 +  2√5

Just use the distance formula 3 times :)