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:

However in the exercises there is this sentence with only went up to & walked up to as correct answers:
She went up to / walked up to the door and rang the doorbell.
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.
I am thankful as always and looking forward to your inputs.