Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{A(0;1)\:\:\:\:\:B(-3;5)\:\:\:\:\:C(1;3)}[/tex]
[tex]\mathsf{M = \left(\dfrac{x_A + x_B}{2};\:\dfrac{y_A + y_B}{2}\right)}[/tex]
[tex]\mathsf{M = \left(\dfrac{0 + (-3)}{2};\:\dfrac{1 + 5}{2}\right)}[/tex]
[tex]\mathsf{M = \left(-\dfrac{3}{2};\:\dfrac{6}{2}\right)}[/tex]
[tex]\mathsf{M = \left(-\dfrac{3}{2};\:3\right)}[/tex]
[tex]\mathsf{\dfrac{NB}{NC} = \dfrac{1}{3}}[/tex]
[tex]\mathsf{N = \left(x_B + \dfrac{x_C - x_B}{4};\:y_B + \dfrac{y_C - y_B}{4}\right)}[/tex]
[tex]\mathsf{N = \left(-3 + \dfrac{1 - (-3)}{4};\:5 + \dfrac{3 - 5}{4}\right)}[/tex]
[tex]\mathsf{N = \left(-3 + \dfrac{1 + 3}{4};\:5 + \dfrac{3 - 5}{4}\right)}[/tex]
[tex]\mathsf{N = \left(-3 + \dfrac{4}{4};\:5 - \dfrac{2}{4}\right)}[/tex]
[tex]\mathsf{N = \left(-3 + 1;\:5 - \dfrac{1}{2}\right)}[/tex]
[tex]\mathsf{N = \left(-2;\:\dfrac{9}{2}\right)}[/tex]
[tex]\mathsf{\dfrac{PA}{PC} = 2}[/tex]
[tex]\mathsf{P = \left(x_C + \dfrac{x_A - x_C}{3};\:y_C + \dfrac{y_A - y_C}{3}\right)}[/tex]
[tex]\mathsf{P = \left(1 + \dfrac{0 - 1}{3};\:3+ \dfrac{1 - 3}{3}\right)}[/tex]
[tex]\mathsf{P = \left(1 - \dfrac{1}{3};\:3 - \dfrac{2}{3}\right)}[/tex]
[tex]\mathsf{P = \left(\dfrac{2}{3};\:\dfrac{7}{3}\right)}[/tex]
[tex]\mathsf{G_{MNP} = \left(\dfrac{x_M + x_N + x_P}{3};\:\dfrac{y_M + y_N + y_P}{3}\right)}[/tex]
[tex]\mathsf{G_{MNP} = \left(\dfrac{(-3/2) + (-2) + (2/3)}{3};\:\dfrac{3 + (9/2) + (7/3)}{3}\right)}[/tex]
[tex]\mathsf{G_{MNP} = \left(\dfrac{-17/6}{3};\:\dfrac{59/6}{3}\right)}[/tex]
[tex]\boxed{\boxed{\mathsf{G_{MNP} = \left(-\dfrac{17}{18};\:\dfrac{59}{18}\right)}}}\leftarrow\textsf{baricentro}[/tex]
