Question

B-verifique se as retas abaixo são paralelas, perpendiculares ou concorrentes oblíquas ​

Answer 1

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

$\Large\boxed{\begin{array}{l}\tt a)~\sf r:4x+6y-10=0\div2\\\sf r: 2x+3y-5=0\implies m_r=-\dfrac{2}{3}\\\\\sf s: 2x+3y-5=0\implies m_s=-\dfrac{2}{3}\\\sf r~e~s~s\tilde ao~coincidentes.\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)~\sf r:2x+3y-4=0\implies m_r=-\dfrac{2}{3}\\\\\sf s:5x-6y-7=0\implies m_s=-\dfrac{5}{-6}=\dfrac{5}{6}\\\sf r~e~s~s\tilde ao~concorrentes.\end{array}}$

$\Large\boxed{\begin{array}{l}\tt c)~\sf r:2x-3y+1=0\implies m_r=-\dfrac{2}{-3}=\dfrac{2}{3}\\\\\sf s:2x-3y+5=0\implies m_s=-\dfrac{2}{-3}=\dfrac{2}{3}\\\sf r\parallel s\end{array}}$

$\Large\boxed{\begin{array}{l}\tt d)~\sf r:2x-y+2=0\implies m_r=-\dfrac{2}{-1}=2\\\sf s:x+2y-4=0\implies m_s=-\dfrac{1}{2}\\\sf m_r\cdot m_s=\backslash\!\!\!2\cdot\bigg(-\dfrac{1}{\backslash\!\!\!2}\bigg)=-1\\\sf r\perp s\end{array}}$

$\Large\boxed{\begin{array}{l}\tt e)~\sf r: x+2y+5=0\implies m_r=-\dfrac{1}{2}\\\\\sf s:3x-2y+1=0\implies m_s=-\dfrac{3}{-2}=\dfrac{3}{2}\\\sf r~e~s~s\tilde ao~concorrentes.\end{array}}$

$\Large\boxed{\begin{array}{l}\tt f)~\sf r: 3x+4y+3=0\implies m_r=-\dfrac{3}{4}\\\\\sf s:3x+4y-7=0\implies m_s=-\dfrac{3}{4}\\\sf r\parallel s\end{array}}$

$\Large\boxed{\begin{array}{l}\tt g)~\sf r:3x-2y+4=0\implies m_r=-\dfrac{3}{-2}=\dfrac{3}{2}\\\\\sf s: 2x+3y-9=0\implies m_s=-\dfrac{2}{3}\\\sf r~e~s~s\tilde ao~concorrentes.\end{array}}$

$\Large\boxed{\begin{array}{l}\tt h)~\sf r:2x+4y-1=0\implies m_r=-\dfrac{2}{4}=-\dfrac{1}{2}\\\\\sf s:4x+8y-2=0\div2\\\sf s:2x+4y-1=0\\\sf r~e~s~s\tilde ao~concidentes\end{array}}$