Not tried it, but I'd just calculate the absolute difference from lower-left lat/long to top-left and AP lat/long values to normalise them to that corner, i.e. lower-left becomes 0,0 in the coordinate system.
Then figure out the scale based on the lower-left top-left difference (I'm simplifying by pretending we're on a plane not a sphere, which for likely floorplans is fine)...
Divide drawing height (in metres) by the lower/top-left latitude difference to get the scaling factor, multiply the AP latitude by that to get AP distance 'up' from lower-left. Use the same scale factor on the AP longitude to get horizontal distance from lower left.
If you sketch things out on a piece of paper with some real values and do the calculations by hand, it'll help see how this works.
It's a quick and dirty method, should be good enough for likely floor sizes away from the poles, if you search online you can find more rigorous methods that take into account that we're (roughly) on a sphere.
