I have coordinates of a city on earth, say latitude: 57.7072326, longitude: 11.9670171. This is city A. I also have coordinates for another city, called city B.
I want to place a marker on these 2 cities on a 2D image. I know the pixel location of city A, and I also know the pixel location of city B.
Now, I get coordinates for a third city, called city C. I do not know the pixel locations of this city, but as I know the pixel locations of 2 other cities, and I can find the relation between the coordinates of city C with A & B, I should be able to find the pixel location of city C. However, always when I do this, my locations are skewed toward either projecting a little bit too far away, and sometimes a little bit too near. What my guess is, that it has to do with the map projection, for example if I am drawing the markers on a Mercator projection, or if it is any other projection.
What my question is, which projection will preserve linearity of coordinates? Is this even possible? A restriction that probably makes this easier is that I am only placing markers on the country of Sweden, and hence there is not a big difference in the coordinate values between the cities (for example, the latitude is around 57 - 65, and longitude is between 11 - 23 for all the cities).