What is x' for Moving Rocket from P?

[Lotto]

TL;DR Summary

Observer S' is in a rocket that is moving relative to an observer S. Outside his rocket happened an event. How to construe the $x'$ of that event? Can be $x'$ negative?

I have a rocket and it is moving straight from a point P with a velocity $v$. When I say that $x'=0$ is at the place we sit in the rocket, then when the event happened outside his rocket at the point P, can I say that the coordinate of the event is for him negative, so $x'=-vt'$, although is it not in his stationary frame of reference?

 

[Ibix]

It depends what the $x$ coordinate of $P$ is which you have not specified, and which frame you are considering $P$ to be at rest in. If $x=0$ and the point is at rest in the unprimed frame then your answer is correct. Generally, you need to use the Lorentz transforms.

 

[obtronix]

Yes it can be negative

In the below space-time diagram enter .6 for velocity, 0 for x, 4 for t for event B.

You will see a negative x' for event B, x' = -3, t'=5

http://www.trell.org/div/minkowski.html