Question

matemática/ Baricentros

1- Determine as coordernadas dos baricentros de um triângulo cujo os vertices são:
a) A(4,2) B(6,8) e C(70,20)
b) A(1,-2) B(5-5) e C(12, -20)
c) A(15,-2) B(5-12) e C(10,-10)​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{G = \{\dfrac{x_A + x_B + x_C}{3};\dfrac{y_A + y_B + y_C}{3}\}}$

$\mathsf{G = \{\dfrac{4 + 6 + 70}{3};\dfrac{2 + 8 + 20}{3}\}}$

$\mathsf{G = \{\dfrac{80}{3};\dfrac{30}{3}\}}$

$\boxed{\boxed{\mathsf{G = \{\dfrac{80}{3};10\}}}}\leftarrow\textsf{letra A}$

$\mathsf{G = \{\dfrac{1 + 5 + 12}{3};\dfrac{-2 - 5 - 20}{3}\}}$

$\mathsf{G = \{\dfrac{18}{3};\dfrac{-27}{3}\}}$

$\boxed{\boxed{\mathsf{G = \{6;-9\}}}}\leftarrow\textsf{letra B}$

$\mathsf{G = \{\dfrac{15 + 5 + 10}{3};\dfrac{-2 - 12 - 10}{3}\}}$

$\mathsf{G = \{\dfrac{30}{3};\dfrac{-24}{3}\}}$

$\boxed{\boxed{\mathsf{G = \{10;-8\}}}}\leftarrow\textsf{letra C}$

Answer 2

• As coordenada dos baricentros podem ser determinada utilizando uma média aritmética entre as coordenadas x e y dos pontos.

A)

$gx = \frac{xa + xb + xc}{3} = \frac{4 + 6 + 70}{3} = {\boxed{\sf \ \red{ \frac{80}{3} }}}$

$gy = \frac{ya + yb + yb}{3} = \frac{2 + 8 + 20}{3} = \frac{30}{3} = {\boxed{\sf \ \red{10}}}$

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B)

$gx = \frac{1 + 5 + 12}{3} = \frac{18}{3} = {\boxed{\sf \ \red{6}}}$

$gy = \frac{ - 2 - 5 - 20}{3} = \frac{ - 27}{3} = {\boxed{\sf \ \red{ - 9}}}$

--------------------------------

C)

$gx = \frac{15 + 5 + 10}{3} = \frac{30}{3} = {\boxed{\sf \ \red{10}}}$

$gy = \frac{ - 2 - 12 - 10}{3} = \frac{ - 24}{3} = {\boxed{\sf \ \red{ - 8}}}$

espero ter ajudado!