Question

dada reta m: 5x - 4y + 7 =0, escreva a reta t perpendicular a reta m passando por p (1 2).

Answer 1

$\large\boxed{\begin{array}{l}\rm m:5x-4y+7=0\\\rm a_{m}=-\dfrac{5}{-4}=\dfrac{5}{4}\\\\\rm s\perp m\iff a_s\cdot a_m=-1\\\rm a_s\cdot\dfrac{5}{4}=-1\\\\\rm a_s=-\dfrac{4}{5}\\\\\rm y=y_0+a_s\cdot(x-x_0)\\\rm y=2-\dfrac{4}{5}\cdot(x-1)\\\\\rm y=2-\dfrac{4}{5}x+\dfrac{4}{5}\bullet(5)\\\\\rm 5y=10-4x+4\\\rm 4x+5y-10-4=0\\\rm s:4x+5y-14=0\end{array}}$