Geometry problem: How to show that the ray is well-defined?

[nontradstuden]

Show that the ray is well defined / independent of ruler placement.

Ruler placement postulate says Given two points P and Q of a line, the coordinate system can be chosen in such a way that the coordinate of P is zero and the coordinate of Q is positive.

I know you can place ray AB where B can be negative or positive, but I don't know where to start or the steps to show a ray's independence.

Thanks for your help.

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A better question is why are rays, line segments, etc independent of the ruler placement postulate? Can you rearrange the points as you please under the new ruler system? Is that why? Like if my points are numbered like A<B<C could it be changed to A<C<B under the new ruler placement?

I'm just trying to understand how rays, segments and such are independent of the ruler placement postulate.

 

[HallsofIvy]

No, absolutely not! It is just the opposite- the ray is independent of the "ruler placement postulate" because if B lies between A and C under one "ruler placement" then B lies between A and C under any "ruler placement".