Answer:
The answer to your question is Perimeter = 26 units
Step-by-step explanation:
Data
Vertex
A(-2, 3)
B (4, 7)
C (7, -1)
Process
1.- Find the distance between the vertex
dAB = [tex]\sqrt{(4 + 2)^{2} + (7-3)^{2}}[/tex]
dAB = [tex]\sqrt{6^{2}+ 4^{2}}[/tex]
dAB = [tex]\sqrt{36 + 16}[/tex]
dAB = [tex]\sqrt{52}[/tex]
dBC = [tex]\sqrt{(7-4)^{2} + (-1 -7)^{2}}[/tex]
dBC = [tex]\sqrt{3^{2} + 8^{2}}[/tex]
dBC = [tex]\sqrt{9 + 64}[/tex]
dBC = [tex]\sqrt{73}[/tex]
dAC = [tex]\sqrt{(7 + 2)^{2}+ (-1-3)^{2}}[/tex]
dAC = [tex]\sqrt{9^{2} + 4^{2}}[/tex]
dAC = [tex]\sqrt{81 + 16}[/tex]
dAC = [tex]\sqrt{97}[/tex]
Perimeter = [tex]\sqrt{52} + \sqrt{73} + \sqrt{97}[/tex]
Perimeter = 7.21 + 8.54 + 9.84
Perimeter = 25.59 ≈ 26 units
