Question

Determine a distância entre o ponto P e a reta r em cada caso:
a) r:4x -3y + 6 = 0 e p (3, 2)
b) r:y = 4x - 5 e p (12, 12)

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf d_{P,r} = |\:\dfrac{ax_0 + by_0 + c}{\sqrt{a^2 + b^2}}\:|$

$\sf r:4x - 3y + 6 = 0 \Leftrightarrow P(3,2)$

$\sf d_{P,r} = |\:\dfrac{4(3) + (-3)2 + 6}{\sqrt{(4)^2 + (-3)^2}}\:|$

$\sf d_{P,r} = |\:\dfrac{12 - 6 + 6}{\sqrt{16 + 9}}\:|$

$\sf d_{P,r} = |\:\dfrac{12}{\sqrt{25}}\:|$

$\boxed{\boxed{\sf d_{P,r} = \dfrac{12}{5}}}$

$\sf d_{P,r} = |\:\dfrac{ax_0 + by_0 + c}{\sqrt{a^2 + b^2}}\:|$

$\sf r:4x - y - 5 = 0 \Leftrightarrow P(12,12)$

$\sf d_{P,r} = |\:\dfrac{4(12) + (-1)12 - 5}{\sqrt{(4)^2 + (-1)^2}}\:|$

$\sf d_{P,r} = |\:\dfrac{48 - 12 - 5}{\sqrt{16 + 1}}\:|$

$\sf d_{P,r} = |\:\dfrac{31}{\sqrt{17}}\:|$

$\boxed{\boxed{\sf d_{P,r} = \dfrac{31\sqrt{17}}{17}}}$