Visuomotor coordination requires both the accurate alignment of spatial information from different sensory streams and the ability to convert these sensory signals into accurate motor commands. Both of these processes are highly plastic, as illustrated by the rapid adaptation of goal-directed movements following exposure to shifted visual feedback. Although visual-shift adaptation is a widely used model of sensorimotor learning, the multifaceted adaptive response is typically poorly quantified. We present an approach to quantitatively characterizing both sensory and task-dependent components of adaptation. Sensory aftereffects are quantified with "alignment tests" that provide a localized, two-dimensional measure of sensory recalibration. These sensory effects obey a precise form of "additivity," in which the shift in sensory alignment between vision and the right hand is equal to the vector sum of the shifts between vision and the left hand and between the right and left hands. This additivity holds at the exposure location and at a second generalization location. These results support a component transformation model of sensory coordination, in which eye-hand and hand-hand alignment relies on a sequence of shared sensory transformations. We also ask how these sensory effects compare with the aftereffects measured in target reaching and tracking tasks. We find that the aftereffect depends on both the task performed during feedback-shift exposure and on the testing task. The results suggest the presence of both a general sensory recalibration and task-dependent sensorimotor effect. The task-dependent effect is observed in highly stereotyped reaching movements, but not in the more variable tracking task.