Question

qual a distância entre os pontos A(7,-1) e B(-5,4)​

Answer 1

✅ Após resolver os cálculos, concluímos que a medida da distância entre os respectivos pontos é:

      $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf D(AB) = 13\,u\:\:\:}}\end{gathered} }$

Sejam os pontos:

                $\Large\begin{cases} A(7, -1)\\B(-5, 4)\end{cases}$

Para calcular a distância entre os referidos pontos temos de usar a seguinte estratégia:

    $\Large\displaystyle\text{ \begin{gathered} D(AB) = \sqrt{(X_{B} - X_{A})^{2} + (Y_{B} - Y_{A})^{2}}\end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \sqrt{(-5 - 7)^{2} + (4 - (-1))^{2}}\end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \sqrt{(-12)^{2} + 5^{2}}\end{gathered} }$

                     $\Large\displaystyle\begin{gathered} = \sqrt{144 + 25}\end{gathered}$

                     $\Large\displaystyle\begin{gathered} = \sqrt{169}\end{gathered}$

                      $\Large\displaystyle\begin{gathered} = 13\end{gathered}$

✅ Portanto, a medida da distância é:

     $\Large\displaystyle\begin{gathered} D(AB) = 13\,u\end{gathered}$

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Veja a solução gráfica representada na figura:

Answer 2

$\Large\displaystyle\text{ \begin{gathered}\tt d_{AB }=\sqrt{(x_{B} -x_{A})^{2}+(y_{B} -y_{A})^{2}}\end{gathered} }$

$\Large\displaystyle\begin{gathered}\tt d_{AB}= \sqrt{(-5-7)^2+(4-(-1))^2}\end{gathered}$

$\Large\displaystyle\begin{gathered}\tt d_{AB}=\sqrt{(-12)^2+(5)^2} \end{gathered}$

$\Large\displaystyle\begin{gathered}\tt d_{AB}= \sqrt{144+25}\end{gathered}$

$\Large\displaystyle\begin{gathered}\tt d_{AB}= \sqrt{169}\end{gathered}$

$\Large\displaystyle\text{ \begin{gathered}\boxed{\tt d_{AB}=13} \end{gathered} }$