Question

Escreva a equação da reta que passa pelo ponto ( 4, -2 ) e é perpendicular à reta r: y = -2x +3

Answer 1

Propriedade de retas perpendiculares :

$\text m_1.\text m_2=-1 \\\\ \underline{\text{onde}} : \\ \text m_1 ,\text m_2 = \text{coeficientes angulares das retas }$

Queremos a reta que passa por ( 4, -2 ) e que é perpendicular à reta :

$\displaystyle \text {r}:\text y = -2\text x+3 \\\\ \text m_1 = -2 \\\\\\ \text{Coeficiente angular da reta que queremos}: \\\\ \text m_1.\text m_2=-1 \\\\ -2.\text m_2 = -1 \to \boxed{ \text m_2= \frac{1}{2}}$

Equação da reta passando por ( 4, -2 ) :

$\displaystyle \text y- \text y_\text o=\text m_2(\text x-\text x_\text o)\\\\\ \text y -(-2) = \frac{1}{2}(\text x-4) \\\\ \text y +2=\frac{(\text x-4)}{2} \\\\ 2\text y+4 = \text x-4 \\\\ \huge\boxed{\text x -2\text y-8 = 0\ }\checkmark$