Honestly I'm with a few of the other posters here: I don't get it.
You obviously can't just project two lat/lon pairs into the plane and then expect to be able to draw a straight line between in the projection coordinate system (x/y) and have the result mean anything, unless those points are extremely close together.
On a Mercator projection that will happen to be a rhumb line, but that's a specific property of that projection.
If you want to know the point halfway along the shortest distance between two lat/lons (and you're prepared to accept the better-but-not-accurate spherical earth model), you can use spherical geometry to determine the mid waypoint along the great circle route.
The futility of thinking otherwise is expressed by the fact that the projection that does map straight lines in the projection to great circles on the globe - i.e. the gnomonic projection - can only show half the world on a map of finite size.
You obviously can't just project two lat/lon pairs into the plane and then expect to be able to draw a straight line between in the projection coordinate system (x/y) and have the result mean anything, unless those points are extremely close together.
On a Mercator projection that will happen to be a rhumb line, but that's a specific property of that projection.
If you want to know the point halfway along the shortest distance between two lat/lons (and you're prepared to accept the better-but-not-accurate spherical earth model), you can use spherical geometry to determine the mid waypoint along the great circle route.
The futility of thinking otherwise is expressed by the fact that the projection that does map straight lines in the projection to great circles on the globe - i.e. the gnomonic projection - can only show half the world on a map of finite size.