The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex] A(-2,\ 2);\ B(5,\ -3)\\\\AB=\sqrt{(5-(-2))^2+(-3-2)^2}=\sqrt{49+25}=\sqrt{74}\\\\A(-2,\ 2);\ C(-4,\ -1)\\\\AC=\sqrt{(-4-(-2))^2+(-1-2)^2}=\sqrt{4+9}=\sqrt{13}\\\\B(5,\ -3);\ C(-4,\ -1)\\BC=\sqrt{(-4-5)^2+(-1-(-3))^2}=\sqrt{81+4}=\sqrt{85}\\\\P_{\triangle ABC}=\sqrt{74}+\sqrt{13}+\sqrt{85} [/tex]
