Question

3- Obtenha as coordenadas do baricentro do triângulo ABC:
a) A(-7,3), B(-8,-4) e C(3,-2)
b) A(0,4), B(8,0) e C(-2,-2)​

Answer 1

As coordenadas dos baricentros dos triângulos são respetivamente G(-4,-1) e G (2, 2/3)

Coordenadas do Baricentro do Triângulo

Encontramos as coordenadas do baricentro do triângulo, calculando a média aritmética dos valores de x e dos valores de y.

$a) A(-7,3), B(-8,-4), C(3,-2)$

   $x_{G} = \frac{-7-8+3}{3} \therefore x_{G} = \frac{-12}{3}\therefore x_{G} = -4$

   $y_{G} = \frac{3-4-2}{3}\therefore y_{G} = \frac{-3}{3}\therefore y_{G} = -1$

   $G (-4,-1)$

$b) A(0,4), B(8,0),C(-2,-2)$

   $x_{G}= \frac{0+8-2}{3}\therefore x_{G}= \frac{6}{3}\therefore x_{G} = 2$

   $y_{G}= \frac{4+0-2}{3}\therefore y_{G}= \frac{2}{3}$

   $G (2,\frac{2}{3})$

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