Unless the stranger has a GPS receiver, the city block coordinate frame is likely to be the most useful.

Back to our exciting virtual world. The displacement
from point A to point B is the vector **v**.
The vector does not depend on any coordinate system.
Using the first coordinate system (middle diagram)
the displacement is represented as

(difference in x coordinates, difference in y coordinates)

In the diagram this is (4, 0)^{T}.
Moving 4 units from point A in the direction of the
x axis brings us to point B.
In the second coordinate system (right diagram)
the same vector is represented by
(2.8, -1.4)^{T}.

Both points and vectors are represented with column matrices. Is this likely to be confusing?