Question

O baricentro de um triângulo é o ponto de encontro das suas medianas, determine as coordenadas do baricentro do triângulo de vértices A ( 2,7), B( 0, -4 ) e C( -8, 9 ) *
a) (-4, 5)
b) (-2, 4)
c) (-3, 6)
d) (-1, 4)

Answer 1

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

$\Large\boxed{\begin{array}{l}\sf A(2,7),B(0,-4),C(-8,9)\\\sf x_G=\dfrac{2+0-8}{3}=\dfrac{-6}{3}=-2\\\\\sf y_G=\dfrac{7-4+9}{3}=\dfrac{12}{3}=4\\\\\sf \red{G(-2,4)}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\red{\maltese}\blue{~alternativa~b}}}}}\end{array}}$