Answer:
The answer to your question is 11.4 units
Step-by-step explanation:
Data
A (-3, -1)
B ( 0, 3)
C ( 1, 2)
Perimeter = ?
Formula
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
Process
1.- Find the length between the points
dAB = [tex]\sqrt{0 + 3)^{2} + (3 + 1)^{2}}[/tex]
dAB = [tex]\sqrt{3^{2}+ 4^{2}}[/tex]
dAB = [tex]\sqrt{9 + 16}[/tex]
dAB = [tex]\sqrt{25}[/tex]
dAB = 5
dBC= [tex]\sqrt{(1 - 0)^{2} + (2 - 3)^{2}}[/tex]
dBC = [tex]\sqrt{1^{2} + (-1)^{2}}[/tex]
dBC = [tex]\sqrt{1 + 1}[/tex]
dBC = [tex]\sqrt{2}[/tex]
dAC = [tex]\sqrt{(1 + 3)^{2} + (2 + 1)^{2}}[/tex]
dAC = [tex]\sqrt{4^{2} + 3^{2}}[/tex]
dAC = [tex]\sqrt{16 + 9}[/tex]
dAC = [tex]\sqrt{25}[/tex]
dAC = 5
2.- Perimeter
P = AB + BC + AC
P = 5 + [tex]\sqrt{2}[/tex] + 5
P = 10 + [tex]\sqrt{2}[/tex]
P = 10 + 1.42
P = 11.4
