how to given numbers to any lines with equal intervals (varying width of interval) as in axes?

Thank you so much @rami. I am really happy to see you, as always you solve my problem.

@rami is it also possible to displace the origin. In the attachment i have displace the origin but points and grid does not displace with them. Pls check and suggest solution.

Once again thanks.

I think this is not possible (sure not possible for the regular axis). And I think too: this make no sense.

But you can define a new free point and then make f and g depending from this new point. Then change also l1 to l5 and maybe more.

Thanks @rami for your support as always. If there is any possibility for origin displace pls do share.

Please tell me what you need it for (so I understand the purpose)

I need to show transformation when bases are different and also both coordinates systems do not have same origin. Also i need to show frame of reference of different moving observers (Like axes moving continuously).

Perhaps this is clearer in 2 separate windows (?)

AND/OR

You need something like this

Hi rami

thanks for this excellent file .

how i can find map for functions or curve in cartesian coordinate to new coordinate in this file or inverse?

Thanks for your support

Unfortunately not one of my core competences.

but here are 2 example from GGBTunbe (transformation, matrices)

https://www.geogebra.org/ma...

https://www.geogebra.org/m/cvmyzugu

Hello @rami, How to add simple numbers in new axes other than coordinates according to x-y axis as in attached.

Thanks rami for your always support. Do you pls explain how the definition of numbering work .

Sequence(Text("" + (XL_2(n)), XL_3(n) - UnitVector(Vector(O, X)) 10pixX + (0, 10pixX)), n, 1, Length(XL_2))

Each number in XL_2 is create as text at position from XL_3. Both elements are addressed with the same (synchronous) index (n). The position (from XL_3) is moved a few pixels in the direction of O and y-axis. The length of 1 pixel is calculated in pixX. If the character size of XL_4 is changed, the factor 10pixX must be adjusted.