Question

Qual é o ângulo formado entre as retas r: y = √3x + 1 e s: y = √3x – 1 ?

Answer 1

Explicação passo-a-passo:

Temos que:

$\sf r:~y=\sqrt{3}x+1~\rightarrow~m_r=\sqrt{3}$

$\sf s:~y=\sqrt{3}x-1~\rightarrow~m_s=\sqrt{3}$

$\sf tg~\alpha=\left|\dfrac{m_r-m_s}{1+m_r\cdot m_s}\right|$

$\sf tg~\alpha=\left|\dfrac{\sqrt{3}-\sqrt{3}}{1+\sqrt{3}\cdot\sqrt{3}}\right|$

$\sf tg~\alpha=\left|\dfrac{0}{1+3}\right|$

$\sf tg~\alpha=\left|\dfrac{0}{4}\right|$

$\sf tg~\alpha=|0|$

$\sf tg~\alpha=0$

Logo, $\sf \alpha=0^{\circ}$

Essas retas são paralelas