Question

1) Determine as coordenadas do baricentro de um triângulo de vértices A(1,6), B(2,-4) e C(6.7).*

a) G (2, 2)
b) G (3,4)
c) G (3,3)
d)G (5.5)​

Answer 1

$\Large\boxed{\begin{array}{l}\sf Sejam~A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf os~v\acute ertices~de~um~tri\hat angulo.\\\sf O~baricentro~do~tri\hat angulo~\acute e~D~\!\!efinido\\\sf pelo~ponto~G(x_G,y_G)\\\sf tal~que~x_G=\dfrac{x_A+x_B+x_C}{3}~e~y_G=\dfrac{y_A+y_B+y_C}{3}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf A(1,6),B(2,-4)~C(6,7)\\\sf x_G=\dfrac{x_A+x_B+x_C}{3}\\\sf x_G=\dfrac{1+2+6}{3}=\dfrac{9}{3}=3\\\sf y_G=\dfrac{y_A+y_B+y_C}{3}\\\sf y_G=\dfrac{6-4+7}{3}=\dfrac{9}{3}=3\\\sf G(3,3)\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~c}}}}\end{array}}$