Question

1.1) Qual a inclinação da reta r: x+y-3=0?
a) 45º
b) 60º
c) 120º
d) 135º
e) 150º

1.2 ) E Qual a equação da reta r que passa pelo pontos E=(2,3) e F=(-4,-3)?

a)r: x+y+1=0
b)r: x-y+1=0
c) r: x-y-1=0
d) r: -x-y+1=0
e) r: -x-y-1=0

Answer 1

Resposta:

1) letra (a) 120°

2) letra (c) r: x+y+1=0

Answer 2

$y=mx+n\\\\ \text{Coeficiente angular}\ \to\ \boxed{m=\tan{\theta}}\\\\ \mathrm{\hat{A}ngulo\ de\ inclina\c{c}\tilde{a}o}\ \to\ \boxed{\theta=\arctan{m}}$

1.1)

$r:x+y-3=0\ \therefore\ y=-x+3\ \therefore\ m=-1\\\\ \theta=\arctan{(-1)}\ \therefore\ \boxed{\theta =135\º}$

1.2)

$E(x_1,y_1)=E(2,3)\\ F(x_2,y_2)=F(-4,-3)\\\\ \boxed{m=\dfrac{dy}{dx}=\dfrac{y_2-y_1}{x_2-x_1}}\ \therefore\ m=\dfrac{-3-3}{-4-2}=\dfrac{-6}{-6}\ \therefore\ m=1$

$y=x+n\ \therefore\ y_1=x_1+n\ \therefore\ 3=2+n\ \therefore\ n=1\\\\ y=x+1\ \therefore\ \boxed{r:x-y+1=0}$