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My question is straightforward. Can the coordinate axes, while being measure by the same unit, be scaled differently (in pure math). Thanks in advance.

Camelot823
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    You can represent graphically the unit of the $x$ axis and the unit of the $y$ axis with different lengths, if needed. – Crostul Aug 24 '22 at 13:16
  • Yes. In fact, they can be scaled differently and be at angles other than $90^{\circ}$. – John Douma Aug 24 '22 at 13:50
  • Welcome to Math.SE! <> When one looks closely, the modern geometric stance is that "scale" is not a property of one set of coordinate axes, but a relationship between two sets of coordinate axes. – Andrew D. Hwang Aug 24 '22 at 14:29
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    It was quite common in 19th century analytic geometry/conics texts to work with what was called "oblique axes" -- see this google-books search. This wasn't an empty exercise in generality, as the use of non-right angle coordinate systems (with equal axis scaling or otherwise) was sometimes used with great ingenuity in some situations. – Dave L. Renfro Aug 24 '22 at 14:29

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