Why are imaginary lines such as longitude and latitude used?

For exactly the same reason that imaginary labels such as "Mulberry Street" and

"416 South" are used. Their purpose is to facilitate the description of locations ...

for the convenience of both the people who are already there and wish to describe

their whereabouts, and the people who are presently elsewhere who wish to journey

to that place.

Note that 'latitude' and 'longitude' are not lines. They are angles. If you mark a

million different points on the Earth's surface that ALL have the same latitude, or

all have the same longitude, THEN the points begin to resemble a line.