Question

calcular a distância entre as retas x-5y-8=0 e x-5y+18=0.

Answer 1

Resposta:

√26

Explicação passo-a-passo:

x - 5y - 8 = 0 (I)

x - 5y = 8 (I)

x - 5y + 18 = 0 (II)

x - 5y = -18 (II)

$d = \frac{|c - c'|}{\sqrt{a^2 + b^2}} \\ \\ d = \frac{|8 -(-18)|}{\sqrt{1^2 + 5^2}} \\ \\ d = \frac{|26|}{\sqrt{26}} \\ \\ d = \frac{26}{\sqrt{26}}.\frac{\sqrt{26}}{\sqrt{26}} \\ \\ d = \frac{26\sqrt{26}}{26} \\ \\ d = \sqrt{26}$