1 arrive
You use arrive or reach to say that someone comes to a place at the end of a journey.
- I'll tell Professor Hogan you've arrived.
- He reached Bath in the late afternoon.
You usually say that someone arrives at a place.
- ...by the time we arrived at Victoria Station.
- ...from the moment he had arrived at the Harlowes' bungalow.
However, you say that someone arrives in a country or city.
- He had arrived in France slightly ahead of schedule.
- The American Ambassador to Mexico arrived in Quito today.
WARNING: You never say that someone 'arrives to' a place.
You also do not say that someone 'arrives at home' or 'arrives in home'. You say that they arrive home.
- we arrived home and I carried my suitcase up the stairs behind her.
You do not use a preposition after arrive in front of here, there, somewhere, or anywhere.
- I arrived here yesterday.
- When we arrived there, we went to the garage.
- Beautiful women, after all, rarely arrive anywhere on time.
2 reach
Reach always takes a direct object. You do not say that someone 'reaches at' a place or that they 'have just reached'.
- It was dark by the time I reached their house.
3 another meaning
Arrive at and reach can both be used to say that someone eventually makes a decision or finds the answer to something.
- It took us several hours to arrive at a decision.
- They were unable to reach a decision.
- I had arrived at a conclusion on the basis of the only facts then available to me.
- The commission could not reach a conclusion because of inadequate data.
Come to can be used in a similar way.
- Kwezi thought for a while, then seemed to come to a decision.
- I came to the conclusion that I could not afford to move.
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