A brain tumor causing alteration of muscle tone, voluntary muscle coordination, gait and balance would likely be located in the:

The cerebellum plays a crucial role in coordinating voluntary muscle movements, maintaining posture, and regulating balance and gait. When a brain tumor affects this area, it can lead to significant alterations in muscle tone, impair voluntary coordination, and disrupt overall balance. These symptoms are indicative of cerebellar dysfunction, aligning perfectly with the functions that the cerebellum regulates.

The other areas mentioned may have specific roles in brain function, but they do not directly correspond with the combination of symptoms described in the question. For instance, the diencephalon is primarily involved in sensory and motor signal relay, as well as regulating functions such as temperature and sleep. The medulla controls autonomic functions like breathing and heart rate, while the pons serves as a communication hub between different parts of the brain but does not specifically govern voluntary motor coordination in the way the cerebellum does. Therefore, the observed symptoms strongly suggest that a brain tumor in the cerebellum would be responsible for the alterations in muscle tone, coordination, gait, and balance.