Question

qual a distância entre o ponto A(-3,2) e B(6,,2)​

Answer 1

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

      $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf D(AB) = 9\,u\:\:\:}}\end{gathered} }$

Sejam os pontos:

                $\Large\begin{cases} A(-3, 2)\\B(6, 2)\end{cases}$

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

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

                      $\Large\displaystyle\text{ \begin{gathered} = \sqrt{(6 - (-3))^{2} + (2 - 2)^{2}}\end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \sqrt{9^{2} + 0^{2}}\end{gathered} }$

                      $\Large\displaystyle\text{ \begin{gathered} = \sqrt[\!\diagup\!]{9^{\!\diagup\!\!\!\!2}}\end{gathered} }$

                      $\Large\displaystyle\begin{gathered} = 9\end{gathered}$

✅ Portanto, a medida da distância é:

     $\Large\displaystyle\begin{gathered} D(AB) = 9\,u\end{gathered}$

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Veja a solução gráfica representada na figura:

Answer 2

$\Large\displaystyle\begin{gathered}\tt d_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\end{gathered}$

$\Large\displaystyle\begin{gathered}\tt d_{AB}=\sqrt{6-(-3))^2+(2-2)^2} \end{gathered}$

$\Large\displaystyle\begin{gathered}\tt d_{AB}= \sqrt{(9)^2+(0)^2}\end{gathered}$

$\Large\displaystyle\begin{gathered}\tt d_{AB}=\sqrt{81+0} \end{gathered}$

$\Large\displaystyle\begin{gathered}\tt d_{AB}=\sqrt{81} \end{gathered}$

$\Large\displaystyle\text{ \begin{gathered}\boxed{\tt d_{AB}=9} \end{gathered} }$