Question

Seja ABC vértices de um triângulo tal que B(3, 1)  e C(5, 3). O ponto G( -4 ; 4) é o baricentro desse triângulo. Determine o ponto A.

Answer 1

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

$\small\boxed{\begin{array}{l}\sf Seja~A(x_A,y_A),B(3,1),C(5,3)~e~G(-4,4).\\\sf x_G=\dfrac{x_A+x_B+x_C}{3}\\\\\sf-4=\dfrac{x_A+3+5}{3}\\\\\sf x_A+8=-12\\\sf x_A=-12-8\\\sf x_A=-20\\\sf y_G=\dfrac{y_A+y_B+y_C}{3}\\\\\sf 4=\dfrac{y_A+1+3}{3}\\\\\sf y_A+4=12\\\sf y_A=12-4\\\sf y_A=8\\\\\sf A(-20,8)\end{array}}$