Question

Calcule a distância entre os dois pontos A (2, -3) e B (4, 3).​

Answer 1

✅ Distância entre dois pontos:

Sejam os pontos:

                $\large\displaystyle\begin{gathered}A(2, -3) \end{gathered}$

                 $\large\displaystyle\begin{gathered}B(4, 3) \end{gathered}$

Obtendo a distância entre os pontos A e B, temos:

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

               $\large\displaystyle\text{ \begin{gathered}= \sqrt{(4 - 2)^{2} + (3 - (-3))^{2} } \end{gathered} }$

               $\large\displaystyle\text{ \begin{gathered}= \sqrt{2^{2} + 6^{2} } \end{gathered} }$

               $\large\displaystyle\begin{gathered}= \sqrt{4 + 36} \end{gathered}$

               $\large\displaystyle\begin{gathered}= \sqrt{40} \end{gathered}$

               $\large\displaystyle\begin{gathered}= 2\sqrt{10} \end{gathered}$

✅ Portanto:

       $\large\displaystyle\text{ \begin{gathered}D_{\overline{AB}} = 2\sqrt{10} \end{gathered} }$

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