He went up to the girl - what does 'up' mean?

Question

I'm not a native English speaker. Sometimes preposition(or adverb) makes me crazy. Look.

He went up to the girl and asked her to dance.
Mr. Jones had to drive up from London to Edinburgh in Scotland.

In these sentences, I don't know what does 'up' mean. I understand what 'up' means in these sentences.

Hands up!
I climbed up to the top of the mountain.

But when we use 'went up to...' What nuance of meaning of the word 'up' is here? So, Because the girl was on the higher place than him, he went 'up' to the girl and asked her to dance?

1. What is difference between 'He went up to the girl' and 'He went to the girl'. Is it possible to omit 'up'? Would it still be the same meaning? What meaning of the word 'up' has here?

2. 'He had to drive up from London to Edinburgh'. In this sentence I think Edinburgh is located more northern than London on the map, So If Edinburgh(I don't know where Edinburgh is) was located more sothern than London, could I write like this: 'He had to drive down from London to Edinburgh'? Am I right?

Answer 1

He went up to the girl.

This means he approached her, probably someone he didn't know, in some social situation.

He went to the girl.

This suggests he had some business with her other than social.

He had to drive up from London to Edinburgh.

"Up" here can suggest either travel to a higher altitude or (by convention) to a more northern location on the map. One would not drive down from London to Edinburgh unless London were at a substantially higher elevation, which it is not. Caveat: Despite what I just said, up and down are often used interchangeably without any such logic being applied. Frequently the preposition over will be used as well:

I went over to Oxford Friday to spend the afternoon with friends.

Answer 2

up is often understood to mean "the entire way".

Prosecutor: Did you step onto the property?
Witness: Yes, I opened the gate and started walking towards the house.
Prosecutor: Did you walk up to the door?
Witness: No, I stopped in the middle of the walkway and went no further.

Consider the following words spoken by a teamster to his mules:

Whoa, there. Hold up!

He means for them to come to a complete stop.

Do you see the semantic relationship between "the entire way" and "complete"?

When we 'fess up or we own up to something, we give a full confession and accept full responsibility. We don't take only partial responsibility or try to weasel our way out of it.

When we man up we summon all of our courage.

And now I should probably shut up and say nothing more.