B What is x' for Moving Rocket from P?

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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?
 
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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.
 
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
 
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