Question

analisando o triângulo abaixo com suas respectivas coordenadas, determine a mediana AM. B(-2,4) A( 4,6) C( 2,-2) M( , )?​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm C\acute alculo\,do\,ponto\,m\acute edio\,dos\,lados\,B\,e\,C:}\\\sf B(-2,4)~~C(2,-2)\\\sf x_M=\dfrac{-2+2}{2}=\dfrac{0}{2}=0\\\\\sf y_M=\dfrac{4+(-2)}{2}=\dfrac{4-2}{2}=\dfrac{2}{2}=1\\\\\sf M(x_M,y_M)\longrightarrow M(0,1)\\\\\underline{\rm C\acute alculo\,da\,mediana\,AM\,do\,tri\hat angulo:}\\\\\sf d_{A,M}=\sqrt{(x_M-x_A)^2+(y_M-y_A)^2}\\\sf d_{A,M}=\sqrt{(0-4)^2+(1-6)^2}\\\sf d_{A,M}=\sqrt{16+25}\\\sf d_{A,M}=\sqrt{41}\end{array}}$