Question

EQUAÇÃO DA RETA R QUE PASSA POR A(2,3) E E PERPENDICULAR A RETA S:X-Y-1=0

Answer 1

Boa noite Paulo!

Solução!\\\\\

$A(2,3)\\\\\ S:x-y-1=0$

Vamos colocar a reta s na forma reduzida para encontramos o coeficiente angular.

$S:x-y-1=0\\\\\ -y=-x+1\\\\ y=x-1\\\\ m=1$

Para que as retas sejam perpendiculares,o coeficiente tem que ser o inverso.

$m(s).m(r)=-1\\\\\ 1.m(r)=-1\\\\ m(r)= \dfrac{-1}{1}\\\\\ m(r)=-1\\\\\\ Equac\~ao ~~da~~reta~~r\\\\\\\ y-yA=m(r)(x-xA)\\\\\\\ y-3=-1(x-2)\\\\\\ y-3=-x+2\\\\\ y=-x+2+3\\\\\ r:y=-x+5\\\\\\ s:x-y-1\perp r:y=-x+5\\\\\\\\ \boxed{Resposta:y=-x+5~~ou~~x+y-5=0}$

Boa noite!
Bons estudos!