Question

Calcule a distância do ponto P(2; 3) à reta r : x + 2y + 2 = 0.

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{r:x + 2y + 2 = 0}$

$\mathsf{P(2;3)}$

$\mathsf{d_{p,r} = |\:\dfrac{a.x_0 + b.y_0 + c}{\sqrt{a^2 + b^2}}\:|}$

$\mathsf{d_{p,r} = |\:\dfrac{(1).(2) + (2).(3) + 2}{\sqrt{(1)^2 + (2)^2}}\:|}$

$\mathsf{d_{p,r} = |\:\dfrac{2 + 6 + 2}{\sqrt{1 + 4}}\:|}$

$\mathsf{d_{p,r} = |\:\dfrac{10}{\sqrt{5}}\:|}$

$\boxed{\boxed{\mathsf{d_{p,r} = 2\sqrt{5}}}}$