How are all paths that have a displacement of zero similar?

Displacement is identified as the net movement of a thing with detail to its initial location. One may journey out of his city and come back. Notwithstanding having enclosed many miles, he will have a displacement of 0. This is true for all trails that have zero displacement that they all go back to their initial position.

Alinear relationship would look like a straight line on the graph. it could have a positive negative or 0 slope. so it could be a line potentially going in any direction but it must be perfectly straight.