を vs で in these sentences

Question

Can't understand Kanji, so please use furigana in answers :)

Context: I'm using Rosetta stone, so there's just pictures. The picture accompanying the first sentence is a girl sleeping on a beach, the picture for the second sentence is just some random guy in mid-stride, walking on top of a mountain.

おんなのこは　かいがんで　ねています

おとこのひとは　やまを　あるいています

I'm confused about the use of で in one and the use of を in the other. As I understand it, で implies wandering around inside some fixed borders, whereas を indicates going through a location.

Would I be right in thinking the first sentence uses で to imply the girl is sleeping on the beach/within the borders of the beach, and を implies the man is walking through the mountains, not within them?

Answer 1

~を together with an motional intransitive verb means "through ~" as you correctly figured out.

~に before an motional verb defines the destination of the movement.

These two uses can't be applied on 寝{ね}る (*) though, because sleeping obviously doesn't contain any motion. I prefer to think of the ~で particle as a "context marker". In which context are you sleeping? In the locational context of the beach. Or another example: かぜで　[学校]{がっこう}を[休]{やす}んだ。 In the context of/because of a cold, I didn't go to school.

(*) As snailboat pointed out, 寝る does not only have the meaning "to sleep", but "to lie down" as well. Of course this is a motion and can be put together with ~に, for example: かいがんに寝る means "to lie down on the beach".