Question

A distância do ponto P(3,2) à reta (r) y = 3x + 2 é:​

Answer 1

Distância do ponto $\underline{\mathsf{P(x_{p},y_{p})}}$ a reta

$\underline{\mathsf{r:~ax+by+c=0}}$

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{d_{P,r}=\dfrac{|ax_{p}+by_{p}+c|}{\sqrt{a^2+b^2}}}}}}}$

$\dotfill$

$\mathsf{r:~y=3x+2\implies~3x-y+2=0}\\\mathsf{d_{P,r}=\dfrac{|ax_{p}+by_{p}+c|}{\sqrt{a^2+b^2}}}\\\mathsf{d_{P,r}=\dfrac{|3\cdot3-1\cdot2+2|}{\sqrt{3^2+2^2}}}\\\mathsf{d_{P,r}=\dfrac{|9-2+2|}{\sqrt{9+4}}}\\\mathsf{d {P,r}=\dfrac{9}{\sqrt{13}}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{d_{P,r}=\dfrac{9\sqrt{13}}{13}}}}}}$

$\dotfill$

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