Question

Considere os pontos A (3,2) e B (8,6) determine as coordenadas de c de um triângulo sabendo que o Baricentro está localizado na origem do plano cartesiano.​

Answer 1

$\large\boxed{\begin{array}{l}\sf Dado~os~pontos~A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf os~v\acute ertices~de~um~tri\hat angulo\\\sf o~Baricentro~deste~tri\hat angulo~\acute e~o~ponto~G(x_G,y_G)\\\sf tal~que\\\sf x_G=\dfrac{x_A+x_B+x_C}{3}~e~y_G=\dfrac{y_A+y_B+y_C}{3}\end{array}}$

$\large\boxed{\begin{array}{l}\sf A(3,2),B(8,6)~G(0,0)~C(x_C,y_C)\\\sf x_G=\dfrac{3+8+x_C}{3}\\\\\sf 3+8+x_C=3x_G\\\sf 11+x_C=3\cdot0\\\sf x_C=-11\\\\\sf y_G=\dfrac{2+6+y_C}{3}\\\\\sf 8+y_C=3y_G\\\\\sf 8+y_C=3\cdot0\\\sf y_C=-8\\\sf C(-11,-8) \end{array}}$