Find the symmetric equations (what am I doing wrong?)

[JoeMathHead]

Find parametric equations for the line. (Use the parameter t.)


The line through the points (0, 1/2, 1) and (5, 1, -8)


I get (5t, (1+t)/2, 1-9t) which is correct


But then it asks:
Find the symmetric equations. And I follow the book and other online help but I get none of these... it happened with another symmetric equations problem too.

I get x/5 = 2y-1 = (1-z)/9 and that isn't one of the options.



Which of the follow is it and why?


1) x − 5 = 2y − 2 = z + 8


2) 2x − 2 = (y − 5)/5 = (z + 8)/(− 9)

3) 5 + 5x = 1 + (y/2) = −8 − 9z

4) (x + 8)/(− 9) = 2y − 2 = (z − 5)/5

5) (x − 5)5 = 2y − 2 = (z + 8)/(− 9)

 

[Imum Coeli]

Is it possible you made a mistake typing 5)? If so, subtract 1 from the answer you obtained.

 

[JoeMathHead]

Is it possible you made a mistake typing 5)? If so, subtract 1 from the answer you obtained.

Nope :/ I typed everything correctly. 5) is correct though, but I still have no clue why. I guessed.

 

[Ishuda]

Choose some t₀, then the symmetric form is
\(\displaystyle \frac{x-5t_0}{5} = {2y - 1 - t_0} = \frac{1 - z - 9t_0}{9}\)
5) is the only one which comes close and I suspect a typo was made in the printing.