Question

3) Prove que as retas s: 2y – 1 = -x + 1   e  r: y = - 1/2 x - 12 são perpendiculares.
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Answer 1

$\mathsf{s:2y-1=-x+1\to~x+2y-1-1=0}\\\mathsf{s:x+2y-2=0\to~m_{s}=-\dfrac{1}{2}}$

$\mathsf{r:y=-\dfrac{1}{2}x-12\to~m_{r} =-\dfrac{1}{2}}$

$\mathsf{r\perp\,s\Leftrightarrow\,m_{r}.m_{s}=-1}$

Vejamos se isso ocorre:

$\mathsf{m_{r}.m_{s}=(-\dfrac{1}{2}).(-\dfrac{1}{2})=\dfrac{1}{4}\ne-1}$

Então essas retas não são perpendiculares.