The kaon electroproduction cross section was extracted from data from the E93-018 and the E01-004 (FPI-2) experiments taken at the Thomas Jefferson National Accelerator Facility in the p(e,eK+)Lambda channel. The cross section was fully separated into longitudinal, transverse, and two interference components at four-momentum transfers Q2 of 1.0 GeV2 (with center of mass energy W=1.81 GeV), 1.36 and 2.07 GeV2 (W=2.31 GeV). The kaon form factor (FK) was extracted from the longitudinal cross section in these kinematics using the Regge model by Vanderhaeghen, Guidal, and Laget. Results show FK to be systematically lower than the empirical monopole form, although still compatible with this form within the estimated uncertainties. The resulting kaon form factor values were combined with the world pion and kaon form factor data to extract the transverse change densities of the pion and kaon. These were compared to that of the proton, showing a possible experimental glimpse of the transition between the proton core and the meson cloud in terms of transverse densities.