Question

Dada a imagem abaixo, determine a equação das retas r e s:

Answer 1

Equação da reta que passa pelo ponto

$\mathsf{P(x_0,y_0)}$ tem coeficiente angular m

$\huge\boxed{\boxed{\boxed{\boxed{\mathsf{y=y_0+m(x-x_0)}}}}}$

$\dotfill$

$\mathsf{m_r=tg(30^{\circ})=\dfrac{\sqrt{3}}{3}}\\\mathsf{y=5+\dfrac{\sqrt{3}}{3}(x-2)}\\\mathsf{y=5+\dfrac{\sqrt{3}}{3}x-\dfrac{2\sqrt{3}}{3}}\\\mathsf{r:y=x\dfrac{\sqrt{3}}{3}-\dfrac{2\sqrt{3}}{3}+\dfrac{15}{3}}\\\mathsf{m_s=tg(135^{\circ})=-1}\\\mathsf{y=5-1(x-2)}\\\mathsf{y=5-x+2}\\\mathsf{s:y=-x+7}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{\maltese~~alternativa~~a}}}}}$