Thank you for the helpful reply. So “I came to an intersection” is the right answer.
Also “arrived at the intersection” (when the intersection is also the destination) and “arrived at a crossroad” are correct. Please do correct me if I am wrong.
You wrote:
‘To’ is a preposition of motion and ‘at’ is a preposition of location. Are there explanations such as these for other prepositions? If so where/which book could I find them in?
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Yes, those are right, ABCDarian. Any good grammar book should have a section on the types of prepositions; you can also google for them, and come up with such sites as THIS ONE. (I called them ‘prepositions of motion’, but here they are called ‘prepositions of direction’.)