Question

Assinale a alternativa que contém a equação da reta que passa pelo ponto P(6,9) e é perpendicular à reta r : 2y - x = 4 no plano cartesiano. *


a) y - x + 21 = 0
b) y + 2x - 21 = 0
c) y + x - 21 = 0
d) y - 2x - 21 = 0
e) y - 2x + 21 = 0

Answer 1

$\boxed{\begin{array}{l}\sf r:2y-x=4\\\sf r:-x+2y-4=0\\\sf m_r=-\dfrac{-1}{2}=\dfrac{1}{2}\\\sf r\perp s\iff m_s\cdot m_r=-1\\\sf m_s\cdot\dfrac{1}{2}=-1\\\sf m_s=2\cdot(-1)\\\sf m_s=-2\\\sf y=y_0+m_s(x-x_0)\\\sf y=9-2\cdot(x-6)\\\sf y=9-2x+12\\\sf y=-2x+21\\\sf s:2x+y-21=0\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~b}}}} \end{array}}$