on the extension of a line; as an extension of
Used both literally for a geometric line extension and figuratively for something that follows naturally from a previous argument, plan, or situation. Often appears as ～の延長線上に(ある/考える).
This point lies on the extension of line segment AB.
This proposal is an extension of our previous discussion.
延長 means 'extension' in general (e.g., time, length). 延長線上 specifically refers to being on the extended line or as a direct continuation of something.
Compound of 延長 (extension) + 線上 (on the line). The figurative use follows naturally from the literal geometric meaning.