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Questions & Answers about Мы живём недалеко от центра.
Why does центр change to центра in this sentence?
The preposition от (from) always requires the Genitive case. Because центр is a masculine noun ending in a consonant, it takes the -а ending. This is similar to the spatial prepositions you are currently learning, like вокруг (around) and вдоль (along), which also require the Genitive.
Can I use из instead of от to say "from the centre"?
No, из wouldn't work here. Из means "out of" and is used when moving out from inside a place. От is used here because it measures a physical distance relative to a starting point, rather than indicating an exit from inside the centre.
Is недалеко always written as a single word?
Most of the time, yes. When it simply means "near" or "not far," it acts as an independent adverb and is one word. You would only write it as two words (не далеко) if there is a strict contrast in the sentence, such as Мы живём не далеко, а близко (We live not far, but close).
Could I say близко от центра to mean the exact same thing?
Yes, близко от (close to) and недалеко от (not far from) mean virtually the same thing and both take the Genitive case. Another very common way to express this idea is рядом с центром (near the centre), which instead uses the preposition с and the Instrumental case.