Question

Calcule a s distancia da reta P à reta r, tendo o ponto P(1,3) e a reta r: 3×+4y-5=0

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Dist\hat ancia~de~um~ponto~P(x_P,y_P)}\\\underline{\rm a~reta~r:ax+by+c=0}\\\\\sf D_{P,r}=\dfrac{| a\cdot x_P+b\cdot y_P+c|}{\sqrt{a^2+b^2}}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf D_{P,r}=\dfrac{| 3\cdot1+4\cdot 3-5|}{\sqrt{3^2+4^2}}\\\\\sf D_{P,r}=\dfrac{|3+12-5|}{\sqrt{9+16}}\\\\\sf D_{P,r}=\dfrac{|10|}{\sqrt{25}}\\\\\sf D_{P,r}=\dfrac{10}{5}\\\\\sf D_{P,r}=2~u\cdot c\end{array}}$