Phrasal verbs meaning 'approach'

[MuiBo]

In my text book, go up to, come up to and walk up to are all listed with the same meaning: "approach".
However in the exercises there is this sentence with only went up to & walked up to as correct answers:

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She went up to / walked up to the door and rang the doorbell. ​

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So I am wondering whether come up to is possible too and if it has any difference in meaning, such as in:

She came up to the door and rang the doorbell. ​

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I am thankful as always and looking forward to your inputs.

 

[heypresto]

You could say 'She came up to the door and rang the doorbell' if you were inside the house, or outside but standing by the door (which I guess is unlikely).

You'd say the other two if you were outside the house.

 

[dojibear]

I agree with post #2. Let me explain:

In general "come" means "move towards the speaker". So you wouldn't say "She came up to the door." unless approaching the door moved her towards you