Answer: [tex]\bold{4+3\sqrt2+\sqrt{10}}[/tex]
Step-by-step explanation:
Perimeter is the sum of the lengths of the sides. Use the distance formula to find the lengths of each of the sides, then find their sum.
[tex]d_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]
[tex]=\sqrt{(-2+1)^2+(1-4)^2}[/tex]
[tex]=\sqrt{(-1)^2+(-3)^2}[/tex]
[tex]=\sqrt{1+9}[/tex]
[tex]=\sqrt{10}[/tex]
[tex]d_{AC}=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}[/tex]
[tex]=\sqrt{(2+1)^2+(1-4)^2}[/tex]
[tex]=\sqrt{(3)^2+(-3)^2}[/tex]
[tex]=\sqrt{9+9}[/tex]
[tex]=\sqrt{18}[/tex]
[tex]=3\sqrt{2}[/tex]
[tex]d_{BC}=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}[/tex]
[tex]=\sqrt{(2+2)^2+(1-1)^2}[/tex]
[tex]=\sqrt{(4)^2+(0)^2}[/tex]
[tex]=\sqrt{16+0}[/tex]
[tex]=\sqrt{16}[/tex]
[tex]=4[/tex]
