So... I have this world map that displays only the seas and landmasses of an earthlike planet. Could you help me place the main mountain ranges where they would make sense according to plate tectonics?
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There is no way to that "make sense". Mountains can be on coastline, like west Americas, inside a continent, like Himalaya or almost isolated, like Kilimanjaro. Geological process are pretty wild and random. Nature don't like to make sense.
You should draw the tectonic map, set the direction they are moving, and after that, you can set the main cordilleras, but a lot of minor mountain chains, like Alps, are not entirely related to this.
Have a look at the Wikipedia on Plate Tectonics
You'll notices that the plates have a very wide range or relationships to the mountain ranges. The Appalachian mountains are nearly in the middle of the North American plate, while the Himalayas are on the edge.
What's unique is that the Himalayas are the only fault line that passes through a major landmass.
Most major landmasses are either center of the plate, or biased to the convergent side which is also usually the west side of the plate.
Islands tend to be anywhere along a fault line.
Partial answer: I see at least three island arcs that ought to be in line with mountain ranges on the adjacent continents.