✅ Após resolver os cálculos, concluímos que a distância entre o ponto "P" e a reta "r" é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf d_{\overline{Pr}} = \frac{24}{5}\:\:\:}}\end{gathered}$}[/tex]
Sejam os dados:
[tex]\Large\begin{cases} P(2, 1)\\r: 4x + 3y + 13 = 0\end{cases}[/tex]
Para calcular a distância entre o ponto "P" e a reta "r", devemos utilizar a seguinte fórmula:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf(I)\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} d_{\overline{Pr}} = \frac{|a_{r}x_{P} + b_{r}y_{P} + c_{r}|}{\sqrt{a_{r}^{2} + b_{r}^{2}}}\end{gathered}$}[/tex]
Substituindo os valores na equação "I", temos:
[tex]\Large\displaystyle\text{$\begin{gathered} d_{\overline{Pr}} = \frac{|4\cdot2 + 3\cdot1 + 13|}{\sqrt{4^{2} + 3^{2}}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \frac{|8 + 3 + 13|}{\sqrt{16 + 9}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \frac{|24|}{\sqrt{25}}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = \frac{24}{5}\end{gathered}$}[/tex]
✅ Portanto, a distância procurada é:
[tex]\Large\displaystyle\text{$\begin{gathered} d_{\overline{Pr}} = \frac{24}{5}\end{gathered}$}[/tex]
[tex]\LARGE\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered}$}[/tex]
Saiba mais:
- https://brainly.com.br/tarefa/46531040
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- https://brainly.com.br/tarefa/49536268
- https://brainly.com.br/tarefa/50055148
- https://brainly.com.br/tarefa/52395667
[tex]\Large\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Observe \:o\:Gr\acute{a}fico!!\:\:\:}}}\end{gathered}$}[/tex]
