Perimeter of triangle ABC is 10.8 units.
Solution:
Given data:
A(-2, -2), B(1, -3) and C(2, 0)
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between AB:
[tex]d=\sqrt{(1-(-2))^2+(-3 -(-2))^2}[/tex]
[tex]d=\sqrt{(1+2)^2+(-3 +2)^2}[/tex]
[tex]d=\sqrt{3^2+(-1)^2}[/tex]
[tex]d=\sqrt{9+1}[/tex]
[tex]d=\sqrt{10}[/tex] units
Distance between BC:
[tex]d=\sqrt{(2-1)^2+(0 -(-3))^2}[/tex]
[tex]d=\sqrt{(1)^2+(3)^2}[/tex]
[tex]d=\sqrt{1+9}[/tex]
[tex]d=\sqrt{10}[/tex] units
Distance between CA:
[tex]d=\sqrt{(2-(-2))^2+(0 -(-2))^2}[/tex]
[tex]d=\sqrt{(2+2)^2+(0+2)^2}[/tex]
[tex]d=\sqrt{4^2+2^2}[/tex]
[tex]d=\sqrt{20}[/tex]
[tex]d=2\sqrt{5}[/tex] units
Perimeter = [tex]\sqrt{10}+\sqrt{10}+2\sqrt{5}[/tex]
[tex]=2\sqrt{10}+2\sqrt{5}[/tex]
= 10.8 units
Perimeter of triangle ABC is 10.8 units.
