Question

Calcule a distancia entre os pontos A (-3,1) e B(-2,2)

Answer 1

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

           $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf D_{\overline{AB}} = \sqrt{2}\:u.c\:\:\:}} \end{gathered} }$

Sejam os pontos:

         $\Large\begin{cases}A(-3, 1)\\B(-2, 2) \end{cases}$

Calculando a distância entre os pontos "A" e "B", temos:

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

                 $\Large\displaystyle\text{ \begin{gathered}= \sqrt{(-2 - (-3))^{2} + (2 - 1)^{2}} \end{gathered} }$

                 $\Large\displaystyle\text{ \begin{gathered}= \sqrt{1^{2} + 1^{2}} \end{gathered} }$

                 $\Large\displaystyle\begin{gathered}= \sqrt{1 + 1} \end{gathered}$

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

✅ Portanto, a distância entre os respectivos pontos é:

        $\Large\displaystyle\text{ \begin{gathered}D_{\overline{AB}} = \sqrt{2}\:u.c \end{gathered} }$

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Answer 2

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

$\Large\displaystyle\text{ \begin{gathered} \sf{ d_{AB}=\sqrt{(-3-(-2))^2+(1-2)^2}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ d_{AB}=\sqrt{(-1)^2+(-1)^2} }\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ d_{AB}=\sqrt{1+1}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \therefore\green{\underline{\boxed{\sf{d_{AB}= \sqrt{2}} }}}~~(\checkmark)\end{gathered} }$