Is there an adjective to describe a road or a river whose orientation is nearly north to south (e.g. looks vertical in the map)? An example sentence would be, "the [word] highway between Foopolis and Barville forms the western border of the State of Ipsumia."
due north, defined by The Free Dictionary
the cardinal compass point that is at 0 or 360 degrees
In your example:
The road running almost due north from Foopolis to Barville forms the western border of the State of Ipsumia.
This isn't a single word, but it is a commonly used and universally understood way of expressing what you are asking.
Perhaps you can use meridian in its adjective form though to me it feels a bit odd to directly apply it on highway.
"the meridian highway between Foopolis and Barville forms the western border of the State of Ipsumia."
The following reworked sentence may be easier to understand:
"the highway along the meridian line between Foopolis and Barville forms the western border of the State of Ipsumia."
[attributive] Relating to or situated at a meridian: ‘the meridian moon’
‘A meridian line is a line used by astronomers, meteorologists and others to measure from.’
‘The meridian line through the Observatory became the official meridian line of Paris.’
NOUN (the adjective definition refers to the noun)
1 A circle of constant longitude passing through a given place on the earth's surface and the terrestrial poles:
‘the European Broadcasting Area extends from the Atlantic to the meridian 40°E’
If a river flows north or south or a road runs south and north (since most roads run both ways) it is coincident with a line of longitude by definition. It is almost certainly coincident with a line of longitude with fractional numbers of degrees (eg 0 degrees 47.32 minutes) but it is still a line of longitude. Therefore it could be said to be longitudinal. A road or river running east-west would be latitudinal, However north-south and east-west for roads and north-flowing, south-flowing and so on are much more colloquial and likely to be understood.
A little insecure on this one, but I'll give it a shot; in fact, two:
How about meridianwise?
(though I understand this would primarily be used as an adverb.)
Hence, my second suggestion: polarward
defined as moving toward polar regions by both Oxford and Merriam Webster, which basically applies to anything that appears “vertical” on the map. I don't really see a metaphor (in case that's the reason for the downvote); merely a widened usage of the concept actually connoted.