Why do we define our axes to be perpendicular to each other?

Geometry Level 2

What could have happened if we redefined planar coordinate geometry with our axes to be inclined at an angle other than \(\frac{\pi}{2}\)?

This problem is inspired by megh choksi

We'd have a new kind of geometry with new sorts of theorems. It would not be a consistent idea because the points on the plane would not have unique coordinates. Nothing at all. We just define it to be \(\frac{\pi}{2}\) to keep things simple. The axes would have projections on each other and would not be independent.

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