Question

Qual as coordenadas do vértice B do triângulo ABC sabendo que seu baricentro tem coordenadas G(8, 5) e que os outros dois vértices são A(8, 5) e C(6, 7).

Answer 1

Explicação passo-a-passo:

As coordenadas do baricentro são dadas por:

$\sf x_G=\dfrac{x_A+x_B+x_C}{3}$

$\sf y_G=\dfrac{y_A+y_B+y_C}{3}$

Assim:

• $\sf x_G=\dfrac{x_A+x_B+x_C}{3}$

$\sf 8=\dfrac{8+x_B+6}{3}$

$\sf 8=\dfrac{x_B+14}{3}$

$\sf x_B+14=3\cdot8$

$\sf x_B+14=24$

$\sf x_B=24-14$

$\sf \red{x_B=10}$

• $\sf y_G=\dfrac{y_A+y_B+y_C}{3}$

$\sf 5=\dfrac{5+y_B+7}{3}$

$\sf 5=\dfrac{y_B+12}{3}$

$\sf y_B+12=3\cdot5$

$\sf y_B+12=15$

$\sf y_B=15-12$

$\sf \red{y_B=3}$

Logo, $\sf B(10,3)$