A distância entre os pontos é dada pela seguinte fórmula:
[tex]\large\displaystyle\text{$\begin{aligned} D=\sqrt{\left( x_B - x_A \right)^2 + \left( y_B - y_A\right)^2} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} A (3,-1) \Rightarrow \begin{cases} x_A = 3 \\ y_A = -1\end{cases} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned}B (3,5) \Rightarrow \begin{cases} x_B = 3 \\ y_B = 5\end{cases} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} D=\sqrt{\left( x_B - x_A \right)^2 + \left( y_B - y_A\right)^2} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} D=\sqrt{\left( 3 - 3 \right)^2 + \left( 5 - (-1)\right)^2} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} D=\sqrt{\left( 0 \right)^2 + \left( 5 +1\right)^2} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} D=\sqrt{0 + \left( 6\right)^2} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} D=\sqrt{ 0 + 36} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned}\therefore \boxed{\boxed{\green{ D=6}}}\end{aligned}$}[/tex]
Distância entre pontos.
[tex]\blue{\square}[/tex] brainly.com.br/tarefa/11540547
✅ Tendo resolvido os cálculos, concluímos que a distância entre os pontos do plano cartesiano é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf d(A,B) = 6\:u.\:c.\:\:\:}}\end{gathered}$}[/tex]
Portanto, a opção correta é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf Alternativa\:B\:\:\:}}\end{gathered}$}[/tex]
Sejam os pontos do plano cartesiano:
[tex]\Large\begin{cases} A(3, -1)\\B(3, 5)\end{cases}[/tex]
Calculando a distância:
[tex]\Large\displaystyle\text{$\begin{gathered} d(A,B) = \sqrt{(X_{B} - X_{A})^{2} + (Y_{B} - Y_{A})^{2}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \sqrt{(3 - 3)^{2} + (5 - (-1))^{2}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \sqrt{0^{2} + (5 + 1)^{2}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \sqrt{0^{2} + 6^{2}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \sqrt{36}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 6\end{gathered}$}[/tex]
✅ Portanto, a distância é:
[tex]\Large\displaystyle\text{$\begin{gathered} d(A, B) = 6\:u.\:c.\end{gathered}$}[/tex]
[tex]\LARGE\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered}$}[/tex]
Saiba mais:
[tex]\Large\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Observe \:o\:Gr\acute{a}fico!!\:\:\:}}}\end{gathered}$}[/tex]
