By treating the homeless man with respect and caring and helping him achieve an optimistic outlook, the police officer, although not a mental health professional, was employing a key principle of: psychogenic treatment. private psychotherapy. positive psychology. eugenics.

Private Psychotherapy.

Explanation:

Psychotherapy is a treatment to help a person with mental ailment by talking with a professional (mental health provider or psychiatrist). It is a therapy that helps a person with mental problem through communication to overcome the problem. This therapy helps the patient to achieve a positive outlook of life.

In the given situation, the police officer is imitating the principles of private psychotherapy. By treating the homeless man with respect, caring, and helping him to have a positive outlook towards life are the principles applied by a psychiatrist or mental health provider to help the person overcome his mental illness.

And, as per the studies, homeless people are more prone to mental illness. Thus, the officer perfomed a private psychotherapy on the homeless person.

Thus the correct answer is Private psychotherapy.