I'm sure somebody has already done this (in fact it's mentioned in http://www.ntsb.gov/info/autopilot_AA77_UA93_study.pdf but I haven't looked back in there yet)
The DCA DME Coords are W077-02.2/N38-51.6
Mapped on G.E.
G.E. reported location of DME is 38.859446 -77.036402
The Ruler distance was 1,080 Feet
This is 1.5NM from the 'pictured' DME location