The Phantom Limb — William Sleator

Isaac is the new kid in town. His mother, Vera, is in the hospital with a mysterious illness, and the only person left to care for Isaac is his distant grandfather. Friendless and often alone, Isaac loses himself in his collection of optical illusions, including a strange mirror box that he finds in his new house, left behind by the previous tenants. Designed for amputees, it creates the illusion of a second limb.

Lonely Isaac wishes someone would reach out to him, and then someone does -- a phantom limb within the mirror box! It signs to Isaac about a growing danger: someone who has murdered before and is out to get Vera next. The only way Isaac can solve the mystery and save his mother is with the help of the mirror box. But can he trust the phantom limb?