Then you would agree with the that, the procedure shown yeilded different results when equal results were demanded; specifically, that the results of going right 3 in one system differs from going left 3 in the opposite system.

RELOCATION occurs when EITHER coincident system moves from mutual coincidence.
TRANSFORMATION occurs when SELECTED points in each system are inserted into the opposte system.

Here is my suggested procedure for THE PROPER selected point transformation between two systems.

Given this depiction

RELOCATING Red left 3 = Blue right is shown direcly below
because we carry the selected points per ( axiom 2 )

Notice; indeed, it is impossibly to tell, from the depiction above, which system was moved and which stayed stationary!

Then IF we elect to do a transformation between systems,
we also get the same results for either Blue left 3 as we do for Red left 3...which this procedure.

Overview...these coincident coordinate questions relate directly to the Galilean coordinate transformation equations, in particular x' - x - vt.

These are coordinates, x and x'... and as such, always stay with their own system and are never ever altered... x in Red = x' in Blue...there is a certainty. Hence the Galilean x' in Blue = x in Red - vt, is most amusing, and also totally wrong. Noting that without this singular equation...there is no Relativity, nor any of all its paradoxes ...
since -vt is THE needed fabrication and their sole cornerstone.

"The Physics of Relativity cannot work, since the Mathematics of their Galilean transformation procedure does not.
Mathematically, once coincident, then x = x' and always must be."
april 13, 2012

email   In particular, if you answered...    no, yes, no    to my three coordinate quiz questions.