Question

Classifique as retas a seguir quanto a posição(concorrentes, paralelas ou perpendiculares)
A) r:=3/2s+1 e s:3x-2y-2=0

B) e:20x-5y-6=0 e s:x+4y+1=0

Answer 1

Caso esteja pelo app, e tenha problemas para visualizar esta resposta, experimente abrir pelo navegador https://brainly.com.br/tarefa/39572582

                                                 

$\large\boxed{\begin{array}{l}\sf Considere~ duas~retas\\\sf\ell_1:m_1x+n_1\\\sf\ell_2:m_2x+n_2\\\underline{\rm ent\tilde ao\!:}\\\sf m_1=m_2~e~n_1\ne n_2\implies\,\ell_1~e~\ell_2~paralelas\\\sf m_1=m_2~e~n_1=n_2\implies\,\ell_1~e~\ell_2~coincidem\\\sf m_1\ne m_2\implies\,\ell_1~e~\ell_2~concorrentes\\\sf m_1\cdot m_2=-1\implies\,\ell_1~e~\ell_2~perpendiculares\end{array}}$

$\large\boxed{\begin{array}{l}\rm A)\\\sf r: y=\dfrac{3}{2}x+1\\\sf s: 3x-2y-2=0\\\sf m_r=\dfrac{3}{2}\\\sf 3x-2y-2=0\\\sf s:~ 2y=3x-2\\\sf s:~ y=\dfrac{3}{2}x-1\\\sf m_s=\dfrac{3}{2} \\\sf m_r= m_s~e~n_r\ne n_s\implies r//s\end{array}}$

$\large\boxed{\begin{array}{l}\rm B)\\\sf r:20x-5y-6=0~~r: y=4x-\dfrac{6}{5}\\\sf m_r=4\\\sf s: x+4y+1=0~~ y=-\dfrac{1}{4}x-\dfrac{1}{4}\\\sf m_s=-\dfrac{1}{4}\\\sf m_r\cdot m_s=\diagup\!\!\!\!4\cdot\bigg(-\dfrac{1}{\diagup\!\!\!\!4}\bigg)=-1\implies r\perp s\end{array}}$