Question

determine o baricentro dos∆:a) a (2,3),b (5,-1), c (-1,4)b) d (-1,0),e (2,-3), e F (2,3)c) h (-1,-4), i (7,6)e J (6,1) d) k (-2,5), L (3,2) e M (5,-7)

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{A(2,3)\iff B(5,-1)\iff C(-1,4)}$

$\mathsf{G_{ABC} = \left(\dfrac{x_A + x_B + x_C}{3};\dfrac{y_A + y_B + y_C}{3}\right)}$

$\mathsf{G_{ABC} = \left(\dfrac{2 + 5 - 1}{3};\dfrac{3 - 1 + 4}{3}\right)}$

$\mathsf{G_{ABC} = \left(\dfrac{6}{3};\dfrac{6}{3}\right)}$

$\boxed{\boxed{\mathsf{G_{ABC} = (2;2)}}}$

$\mathsf{D(-1,0)\iff E(2,-3)\iff F(2,3)}$

$\mathsf{G_{DE{F}} = \left(\dfrac{x_D + x_E + x_F}{3};\dfrac{y_D + y_E + y_F}{3}\right)}$

$\mathsf{G_{DE{F}} = \left(\dfrac{-1 + 2 + 2}{3};\dfrac{0 - 3 + 3}{3}\right)}$

$\mathsf{G_{DE{F}} = \left(\dfrac{3}{3};\dfrac{0}{3}\right)}$

$\boxed{\boxed{\mathsf{G_{DE{F}} = (1;0)}}}$

$\mathsf{H(-1,-4)\iff I(7,6)\iff J(6,1)}$

$\mathsf{G_{HIJ} = \left(\dfrac{x_H + x_I + x_J}{3};\dfrac{y_H + y_I + y_J}{3}\right)}$

$\mathsf{G_{HIJ} = \left(\dfrac{-1 + 7 + 6}{3};\dfrac{-4 + 6 + 1}{3}\right)}$

$\mathsf{G_{HIJ} = \left(\dfrac{12}{3};\dfrac{3}{3}\right)}$

$\boxed{\boxed{\mathsf{G_{HIJ} = (4;1)}}}$

$\mathsf{K(-2,5)\iff L(3,2)\iff M(5,-7)}$

$\mathsf{G_{KLM} = \left(\dfrac{x_K + x_L + x_M}{3};\dfrac{y_K + y_L + y_M}{3}\right)}$

$\mathsf{G_{KLM} = \left(\dfrac{-2 + 3 + 5}{3};\dfrac{5 + 2 - 7}{3}\right)}$

$\mathsf{G_{KLM} = \left(\dfrac{6}{3};\dfrac{0}{3}\right)}$

$\boxed{\boxed{\mathsf{G_{KLM} = (2;0)}}}$