Question

3-Calcule o baricentro do triângulo ABC,de vértices A(-4,-5),B(-1,6) e C(3,-2)

Answer 1

Olá Jaqueline 

A(-4,-5), B(-1,6), C(3,-2)

Gx = (Ax + Bx + Cx)/3

Gx = (-4 - 1 + 3)/3 = 2/3 

Gy = (Ay + By + Cy)/3

Gy = (-5 + 6 - 2)/3 = -1/3 

G(2/3,1/3) 

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Answer 2

✅ Após resolver os cálculos, concluímos que o baricentro "G" é:

           $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf G = \Bigg(\frac{-2}{3}, \frac{-1}{3} \Bigg)\:\:\:}}\end{gathered} }$

Sejam os pontos:

                  $\Large\begin{cases}A = (-4, -5)\\ B = (-1, 6)\\C = (3, -2)\end{cases}$

Para calcular o baricentro "G" do triângulo devemos calcular a média aritmética de suas abscissas e ordenadas, ou seja:

  $\Large\displaystyle\text{ \begin{gathered} G = \Bigg(\frac{X_{A} + X_{B} + X_{C}}{3}, \frac{Y_{A} + Y_{B} + Y_{C}}{3} \Bigg)\end{gathered} }$

      $\Large\displaystyle\begin{gathered} = \Bigg(\frac{-4 - 1 + 3}{3}, \frac{-5 + 6 - 2}{3} \Bigg)\end{gathered}$

      $\Large\displaystyle\begin{gathered} = \Bigg(\frac{-2}{3}, \frac{-1}{3} \Bigg)\end{gathered}$

Portanto, o baricentro é:

       $\Large\displaystyle\begin{gathered} G = \Bigg(\frac{-2}{3}, \frac{-1}{3} \Bigg)\end{gathered}$

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