Question

Diferença entre ponto e reta sendo p (0,2) e R=4x-3y-11=0

Answer 1

$\text{d}=\dfrac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}$

Nessa questão temos:

$a=4~~~~~~~~b=-3~~~~~~~~c=-11~~~~~~~x_0=0~~~~~~~y_0=2$

Então, a distância procurada é:

$\text{d}=\dfrac{|4\cdot0+(-3)\cdot2+(-11)|}{\sqrt{4^2+(-3)^2}}$

$\text{d}=\dfrac{|0-6-11|}{\sqrt{16+9}}$

$\text{d}=\dfrac{|-17|}{\sqrt{25}}$

$\text{d}=\dfrac{17}{5}$

$\text{d}=3,4$