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when does projection matter?

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Hello all, this question may seem rudimentary, but Its been bugging me and I want to confirm.

If say I have 2 polygon layers, zipcode and city boundary for example, and I want to clip the zipcodes using my city boundary, does it matter what projection I do it in (assuming both layers have the same projection)? I.e. if Zipcode X is inside my city boundary using web mercator, it will still be inside my city boundary if I switch both layers to any other projection?. The projection will only change physical measurements such as distances and areas but not the relative relationship between my polygons.

thank you all for the help

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