Question

Dadas as equações r: 2x+4y+5=0 e s: y=-2x+3, marque a alternativa correta:

Answer 1

Posição relativa de duas retas

Considere duas retas

$\mathsf{\ell_{1}:m_{1}x+n_{1}}\\\mathsf{\ell_{2}:m_{2}x+n_{2}}$.

Então

$\mathsf{m_{1}=m_{2}~e~n_{1}\ne n_{2}\implies\,\ell_{1}~e~\ell_{2}~paralelas}\\\mathsf{m_{1}=m_{2}~e~n_{1}=n_{2}\implies\,\ell_{1}~e~\ell_{2}~coincidem}\\\mathsf{m_{1}\ne m_{2}\implies\,\ell_{1}~e~\ell_{2}~concorrentes}\\\mathsf{m_{1}\cdot m_{2}=-1\implies\,\ell_{1}~e~\ell_{2}~perpendiculares}$

$\dotfill$

$\mathsf{r:~2x+4y+5=0\implies~m_r=-\dfrac{1}{2}}\\\mathsf{s:~y=-2x+3\implies~m_s=-2}\\\mathsf{m_r\ne m_s\implies r\times s}$

Verifique o gabarito

$\dotfill$

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