Question

4)A distância do ponto P (2,8) à reta da equação 5x-12y+1=0 é :

5)A distância do ponto P (-3,4)à reta da equação 3x+4y+1=0 é :​

Answer 1

$\Large\boxed{\begin{array}{l}\rm Dado~um~ponto~P(x_p,y_p)~a~dist\hat ancia~de~\\\rm P~\grave a~reta~r:~ax+by+c=0~\acute e~dada~por\\\rm D_{P,r}=\dfrac{|a x_p+by_p+c|}{\sqrt{a^2+b^2}}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf P(2,8)~~r:5x-12y+1=0\\\sf D_{P,r}=\dfrac{|5\cdot2-12\cdot8+1|}{\sqrt{5^2+(-12)^2}}\\\\\sf D_{P,r}=\dfrac{| 10-96+1|}{\sqrt{25+144}}\\\\\sf D_{P,r}=\dfrac{85}{\sqrt{169}}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf D_{P,r}=\dfrac{85}{13}}}}}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf P(-3,4)~~r:~3x+4y+1=0\\\sf D_{P,r}=\dfrac{|3\cdot(-3)+4\cdot4+1|}{\sqrt{(-3)^2+4^2}}\\\\\sf D_{P,r}=\dfrac{|-9+16+1|}{\sqrt{9+16}}\\\\\sf D_{P,r}=\dfrac{8}{\sqrt{25}}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf D_{P,r}=\dfrac{8}{5}}}}}\end{array}}$