Olá!
Temos:
[tex]A(0,0),\:\:B(3,7)\:\:e\:\:C(5,-1)[/tex]
Agora, vamos determinar as coordenadas de M, vejamos:
[tex]x_M = \dfrac{x_B+x_C}{2} \to x_M = \dfrac{3+5}{2} \to x_M = \dfrac{8}{2} \to \boxed{x_M =4}[/tex]
[tex]y_M = \dfrac{y_B+y_C}{2} \to y_M = \dfrac{7+(-1)}{2} \to y_M = \dfrac{6}{2} \to \boxed{y_M =3}[/tex]
[tex]M (4,3)[/tex]
Agora, vamos encontrar a medida AM, vejamos:
[tex]d_{AM} = \sqrt{(x_A-x_M)^2+(y_A-y_M)^2} [/tex]
[tex]d_{AM} = \sqrt{(0-4)^2+(0-3)^2} [/tex]
[tex]d_{AM} = \sqrt{(-4)^2+(-3)^2}[/tex]
[tex]d_{AM} = \sqrt{16+9}[/tex]
[tex]d_{AM} = \sqrt{25}[/tex]
[tex]\boxed{\boxed{d_{AM} = 5}}\end{array}}\qquad\checkmark[/tex]
Espero ter ajudado!
