I could see him killing her there though. Her staring out at "his works", and freaking out, and he just does it. Or her refusal of his gift, his eden, and it gets messy. He seemed highly upset standing there and being near the marker. He did say he thought it was a good place for her, so likely that would be the nicest spot he could think of to do it.
I think that's the exact spot where she died.