Final answer:
Legally, a person may take the life of another only in self-defense when faced with an immediate threat to their own life. Other scenarios provided do not justify lethal action, and the law includes protections such as in cases of insanity or where there is no intent to kill.
Step-by-step explanation:
The conditions under which a person may take the life of another person are strictly defined by law and are generally very limited. The only scenario presented here which may legally justify taking another person's life is in self-defense, when there's an imminent and unlawful threat to one's own life (option 3). It's important to note that the legal standards for what constitutes legitimate self-defense can vary by jurisdiction and usually require that the force used in defense be proportionate to the threat posed. Options 1, 2, and 4 do not justify taking another person's life. The idea of taking one person's life to prolong another's is specifically addressed in cases such as Ford v. Wainwright, where the imposition of a death sentence on an insane person is prohibited, and Enmund v. Florida, where the death sentence can't be imposed on those who didn't kill or intend to kill.