Question

Sabendo que P1 = (- 1/9, 0, 10/9) e P2 = (1/9, 0, 8/9) a distância entre os pontos P1 e P2 é:

Answer 1

✅ Após resolver os cálculos, concluímos que a distância entre os referidos pontos é:

  $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf D(P_{1}P_{2}) = \frac{2\sqrt{2}}{9}\:u\cdot c\:\:\:}}\end{gathered} }$

Sejam os pontos:

          $\Large\displaystyle\begin{gathered} P_{1} = \bigg(-\frac{1}{9},\,0,\,\frac{10}{9}\bigg)\end{gathered}$

          $\Large\displaystyle\begin{gathered} P_{2} = \bigg(\frac{1}{9},\,0,\,\frac{8}{9}\bigg)\end{gathered}$

Para calcular a distância entre estes pontos fazemos:

 $\large\displaystyle\text{ \begin{gathered} D(P_{1}P_{2}) = \sqrt{(X_{P_{2}} - X_{P_{1}})^{2} + (Y_{P_{2}} - Y_{P_{1}})^{2} + (Z_{P_{2}} - Z_{P_{1}})^{2}}\end{gathered} }$

                  $\Large\displaystyle\text{ \begin{gathered} = \sqrt{\bigg(\frac{1}{9} -\bigg(-\frac{1}{9}\bigg)\bigg)^{2} + (0 - 0)^{2} + \bigg(\frac{8}{9} - \frac{10}{9}\bigg)^{2}}\end{gathered} }$

                  $\Large\displaystyle\text{ \begin{gathered} = \sqrt{\bigg(\frac{1}{9} + \frac{1}{9}\bigg)^{2} + 0^{2} + \bigg(\frac{8}{9} - \frac{10}{9}\bigg)^{2}}\end{gathered} }$

                  $\Large\displaystyle\text{ \begin{gathered} = \sqrt{\bigg(\frac{2}{9}\bigg)^{2} + \bigg(-\frac{2}{9}\bigg)^{2}}\end{gathered} }$

                  $\Large\displaystyle\text{ \begin{gathered} = \sqrt{\frac{2^{2}}{9^{2}} + \frac{(-2)^{2}}{9^{2}}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \sqrt{\frac{4}{81} + \frac{4}{81}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \sqrt{\frac{8}{81}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{8}}{\sqrt{81}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \frac{2\sqrt{2}}{9}\end{gathered} }$

✅ Portanto, a distância procurada é:

       $\Large\displaystyle\text{ \begin{gathered} D(P_{1}P_{2}) = \frac{2\sqrt{2}}{9}\:u\cdot c\end{gathered} }$

Saiba mais:

1. https://brainly.com.br/tarefa/49810376
2. https://brainly.com.br/tarefa/49909620
3. https://brainly.com.br/tarefa/49916771
4. https://brainly.com.br/tarefa/50257292
5. https://brainly.com.br/tarefa/50274175
6. https://brainly.com.br/tarefa/43252404
7. https://brainly.com.br/tarefa/51021572
8. https://brainly.com.br/tarefa/51167799
9. https://brainly.com.br/tarefa/6452005
10. https://brainly.com.br/tarefa/7634213
11. https://brainly.com.br/tarefa/51453720
12. https://brainly.com.br/tarefa/51453717
13. https://brainly.com.br/tarefa/51481076
14. https://brainly.com.br/tarefa/51571297
15. https://brainly.com.br/tarefa/51693963

Solução gráfica (figura):