Question

02- Calcule a distância do ponto P(1,-5) à reta r: 3x + 4y - 2 = 0.
a) 18/2
b) 19/3
c) 20/4
d) 2115

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{3x + 4y - 2 = 0}$

$\mathsf{P(1;-5)}$

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

$\mathsf{d_{p,r} = |\:\dfrac{3.(1) + 4.(-5) + (-2)}{\sqrt{(3)^2 + (4)^2}}\:|}$

$\mathsf{d_{p,r} = |\:\dfrac{3 - 20 - 2}{\sqrt{9 + 16}}\:|}$

$\mathsf{d_{p,r} = |\:\dfrac{-19}{\sqrt{25}}\:|}$

$\boxed{\boxed{\mathsf{d_{p,r} = \dfrac{19}{5}}}}$