They project the surface of a sphere (the Earth) using a projection. Often the latitudes and longitudes are mapped onto the coordinate plane for small area but such projections distort shapes when mapping larger areas.
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Yes, almost all the time. And when it is not coordinate planes it is coordinate hype-spaces (more than just the 2 dimensions that the coordinate plane allows).
Yes, they are.
It was Rene Decartes
it is when you go to a career and you learn about cordinate planes
Designing, mapping, cartography, meteorology are some.