  Abridged: We have used the well-selected sample of ~1750 embedded, young,
massive stars identified by the RMS survey to investigate the Galactic
distribution of recent massive star formation. We describe the various methods
used to assign distances extracted from the literature, and solve the distance
ambiguities towards ~200 sources located within the Solar circle using archival
HI data. These distances are used to calculate bolometric luminosities and
estimate the survey completeness (~2x10^4 lsun). In total, we calculate the
distance and luminosity of ~1650 sources, one third of which are above the
survey's completeness threshold. Examination of the sample's longitude,
latitude, radial velocities and mid-infrared images has identified ~120 small
groups of sources, many of which are associated with well known star formation
complexes, such as W43, W49 and W51.
  We compare the positional distribution of the sample with the expected
locations of the spiral arms, assuming a model of the Galaxy consisting of four
gaseous arms. The distribution of young massive stars in the Milky Way is
spatially correlated with the spiral arms, with strong peaks in the source
position and luminosity distributions at the arms' Galactocentric radii. The
overall source and luminosity surface densities are both well correlated with
the surface density of the molecular gas, which suggests that the massive star
formation rate per unit molecular mass is approximately constant across the
Galaxy.
  We estimate the total luminosity of the embedded massive star population to
be ~0.76x10^8 lsun, 30% of which is associated with the ten most active star
forming complexes. We measure the scale height as a function of Galactocentric
distance and find that it increases only modestly from ~20-30 pc between 4 and
8 kpc, but much more rapidly at larger distances.
