Respuesta :
Answer: P≈14,15.
Step-by-step explanation:
Line length formula:
[tex]\overline {L}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]P=\overline {AB}+\overline {BC}+\overline {AC}\\A(3;1)\ \ \ \ \ B(2;-1)[/tex]
[tex]x_1=3\ \ \ \ x_2=2\ \ \ \ y_1=1\ \ \ \ y_2=-1\\\\\overline {AB}=\sqrt{(2-3)^2+(-1-1)^2}\\\\ \overline {AB}=\sqrt{(-1)^2+(-2)^2}\\\\ \overline {AB}=\sqrt{(1+4}\\\\ \overline {AB}=\sqrt{5}.\\\\[/tex]
[tex]B(2;-1)\ \ \ \ C(-3;2)\\\\x_1=2\ \ \ \ \ x_2=-3\ \ \ \ y_1=-1\ \ \ \ y_2=2\\\\\overline {BC}=\sqrt{(-3-2)^2+(2-(-1))^2}\\\\\overline {BC}=\sqrt{(-5)^2+(2+1)^2}\\\\\overline {BC}=\sqrt{25+3^2}\\\\\overline {BC}=\sqrt{25+9}\\\\\overline {BC}=\sqrt{34}.\\\\[/tex]
[tex]A(3;1)\ \ \ \ C(-3;2)\\\\x_1=3\ \ \ \ \ x_2=-3\ \ \ \ y_1=1\ \ \ \ \ \ y_2=2\\\\\overline {AC}=\sqrt{(-3-3)^2+(2-1)^2} \\\\\overline {AC}=\sqrt{(-6)^2+1^2} \\\\\overline {AC}=\sqrt{36+1} \\\\\overline {AC}=\sqrt{37}. \\\\[/tex]
[tex]P=\sqrt{5}+\sqrt{34} +\sqrt{37} \\\\P\approx14,15.[/tex]
