Question

Encontre as coordenadas do vértice A de um triângulo ABC, sendo o baricentro G (2, 8/3), vértice B (-1, 3) e C (6, 4)

Answer 1

$\mathrm{Tri\^angulo\ \to\ A(x_A,y_A);B(-1,3);C(6,4)}\\ \mathrm{Baric\^entro\ \to\ G(x_G,y_G)=G(2,8/3)}\\\\ \mathrm{x_G=\dfrac{x_A+x_B+x_C}{3}\ \to\ 2=\dfrac{x_A+(-1)+6}{3}}\\\\ \mathrm{2.3=x_A-1+6\ \to\ 6=x_A+5\ \to\ \boxed{\mathbf{x_A=1}}}\\\\ \mathrm{y_G=\dfrac{y_A+y_B+y_C}{3}\ \to\ \dfrac{8}{3}=\dfrac{y_A+3+4}{3}}\\\\ \mathrm{8=y_A+7\ \to\ \boxed{\mathbf{y_A=1}}}\\\\ \boxed{\boxed{\mathbf{A(1,1)}}}$