You don't always replace X and Y (as in coordinates) to something longer. I know, they can be (and probably should be) replaced with left/right and top/bottom when we are talking about boxes, but not all X and Y can be replaced.

You replace them with abscissa and ordinate actually. And Z will be applicate, it seems, although I already heard azimuth used for this one. I'm not aware of a dedicated terms for higher dimensions, so your beautiful (w,x,y,z) quaternion tuple is a big deal, isn't it.

Anyway, you can always use an array `coordinates` with whatever dimensions you want.

Sure, but those are commonly used names and well established, so they act as actual, proper words in this kind of discussion. There are some widely accepted short names that can still be descriptive.

But arbitrary abbreviations like "tk" don't fall into this category.

You need some basic understanding of 2D graphics to understand what is X and Y. In fact, they are not good names otherwise because it is pretty easy to mix them up---one more reason to prefer left/right/top/bottom whenever possible. I've seen some codes using Column and Row instead of X and Y for that very reason. (Not to say that I like it.)

If you are okay with X and Y, you should probably have to accept that the definition of "commonly used", "well established" and "actual, proper" words is subjective and different areas and projects have different notions of them. I'm okay with `tk` if it is used consistently and doesn't interfere otherwise.

Yes they do. tk, pc, sp, a, etc all fall into the well established category in this context.