The big issue with plotting maps is that the spherical surface of the Earth cannot be conveniently converted into a flat representation. There are a bunch of different projections that attempt to resolve this.
Mercator is one of the simplest: it assumes that lines of equal latitude are parallel horizontals, while lines of equal longitude are parallel verticals. This is valid for latitude (1 degree of latitude approximately equals 111 km no matter where you are), but not valid for longitude (the surface distance of a degree of longitude is proportional to the cosine of the latitutude).
However, as long as you’re below about 45 degrees (which most of Minnesota is), a Mercator projection works very well, and creates the forms that most people will recognize from their grade school maps. And it’s very simple: just treat the points as absolute coordinates, and scale to whatever space you’re drawing them in. No trig necessary.