This paper presents a method for determining the six degree-of-freedom transformation between a camera and a base frame of interest. A planar mirror is maneuvered so as to allow the camera to observe the environment from several viewing angles. Points, whose coordinates in the base frame are known, are observed by the camera via their reflections in the mirror. Exploiting these measurements, we determine the camera-to-base transformation analytically, without assuming prior knowledge of the mirror motion or placement with respect to the camera. The computed solution is refined using a maximum-likelihood estimator, to obtain high-accuracy estimates of the camera-to-base transformation and the mirror configuration for each image.We validate the accuracy and correctness of our method with simulations and real-world experiments.