We invert geodetic measurements of coseismic surface displacements to determine a dislocation model for the April 25, 1992, M=7 Cape Mendocino, California, earthquake. The orientation of the model slip vector, which nearly parallels North America--Juan de Fuca relative plate convergence, and the location and orientation of the model fault relative to the offshore Cascadia megathrust, suggest that the 1992 Cape Mendocino earthquake is the first well-recorded event to relieve strain associated with the Cascadia subduction zone. We use data from three geodetic techniques: (1) the horizontal and vertical displacements of 13 monuments surveyed with the Global Positioning System, corrected for observed horizontal interseismic strain accumulation, (2) 88 section-elevation differences between leveling monuments, and (3) the uplift of 12 coastal sites observed from the die-off of intertidal marine organisms. Maximum observed displacements are 0.4 m of horizontal movement and 1.5 m of uplift along the coast. We use Monte Carlo techniques to estimate an optimal uniform slip rectangular fault geometry and its uncertainties. The optimal model using all the data resolves 4.9 m of slip on a 14 by 15 km fault that dips 28¿ SE. The fault extends from 1.5 to 8.7 km in depth and the main-shock hypocenter is close to the downdip projection of the fault. The shallowly dipping fault plane is consistent with the observed aftershock locations, and the estimated geodetic moment is 3.1¿1019 N m, 70% of the seismic moment. Other models that exclude leveling data collected in 1935 and 1942 are more consistent with seismological estimates of the fault geometry. If the earthquake is characteristic for this segment, the estimated horizontal slip vector compared with plate convergence rates suggests a recurrence interval of 140 years, with a 95% confidence range of 100--670 years. The coseismic uplift occurred in a region that also has high Quaternary uplift rates determined from marine terrace studies. If repeated ruptures of this southernmost segment of the Cascadia megathrust are responsible for the Quaternary uplift, a comparison of the coseismic uplift with coastal uplift rates suggests a recurrence interval of 200--400 years. Thus comparing horizontal and vertical coseismic to long-term deformation suggests a recurrence interval of about 100--300 years for M=7 events at the south end of the Cascadia megathrust.