Final answer:
The ethical principle associated with an adult child legally given the right to make medical decisions for a cognitively impaired parent is the Principle of autonomy.
Step-by-step explanation:
The ethical principle associated with an adult child legally given the right to make medical decisions for a cognitively impaired parent is Principle of autonomy. The principle of autonomy states that patients have a right to exercise agency or self-determination when it comes to making decisions about their own health care in clinical settings. In this case, the adult child is acting as a surrogate decision-maker for the parent who is unable to make decisions due to cognitive impairment. By acting in the best interest of the parent, the adult child is upholding the principle of autonomy.