In this work we describe a teaching proposal to calculate the eccentricity of the Moon's trajectory by applying a geometrical technique. The values of the ratios between the Earth-Moon distance and the diameter of the Moon at apogee and at perigee were calculated from a kinematic model associated with a geometrical technique of image analysis. The experimental data were collected from two videos of the Moon's movement in positions close to the apogee and perigee. We chose two frames of both videos, and by means of image analysis we obtained a geometrical parameter for each video and by means of a kinematic model we defined a physical parameter. Then, by combining both parameters we calculated the maximal and minimum apparent diameters, which were used to calculate the eccentricity. Finally, we compared our results with values of literature.