'How to set a different axes system on a matplotlib plot?

I have a matplotlib plot on which I found the coordinates of given points like this: enter image description here

I am trying to find a way to add different axes on the same plot, and get the coordinates of the same points but according to the new axis system, like this: enter image description here

I am very much a python beginner and I have been struggling with this. Is there a way to do that ?



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