Question

1 - Calcule e indique a distância entre o ponto P(0, 10) e a reta s: x - y + 1 = 0.:
a) 9V2 2
b) 9V3 2
c) 8V2 3
)9V5 2​

Answer 1

Explicação passo-a-passo:

$\sf d=\dfrac{|a\cdot x_0+b\cdot y_0+c|}{\sqrt{a^2+b^2}}$

$\sf d=\dfrac{|1\cdot0+(-1)\cdot10+1|}{\sqrt{1^2+(-1)^2}}$

$\sf d=\dfrac{|0-10+1|}{\sqrt{1+1}}$

$\sf d=\dfrac{|-9|}{\sqrt{2}}$

$\sf d=\dfrac{9}{\sqrt{2}}$

$\sf d=\dfrac{9}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf d=\dfrac{9\sqrt{2}}{2}$

Letra A