What is the meaning of the preposition 'in' this below sentence? What relationship does it serve to indicate?
Her house lies in that direction.
Is it idiomatic?
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In is an old word and has many uses.
Cambridge has in preposition (ᴀʀʀᴀɴɢᴇᴍᴇɴᴛ)
used to show how things or people are arranged or divided:
- We all sat down in a circle.
- The desks were arranged in rows of ten.
It can be seen that "in that direction" has a similar sense: "We all sat down in that direction"; "The desks were laid out in that direction."
OED has 12b. "Of form, shape, conformation, order", and shows this usage dates from Old English.
So, no: it's not idiomatic. In can be used to show how things are arranged in relationship to each other.
Merriam Webster says:
1a —used as a function word to indicate inclusion, location, or position within limits
In your example, "in the north" indicates location or position within limits