extremity
The farthest part of something, or the most extreme point.
An extremity is the farthest point or edge of something, or the most intense degree of a situation. Your fingers and toes are called extremities because they're at the ends of your limbs, the farthest points from your heart. The northern extremity of Alaska reaches deep into the Arctic Circle, while the southern extremity of South America nearly touches Antarctica.
The word also describes extreme conditions or desperate circumstances. During the extremity of a harsh winter, people might face dangerous cold and scarce food supplies. In the extremity of their fear, trapped hikers might make risky decisions they'd normally avoid. When someone is pushed to extremities, they're facing such serious trouble that they might do things they wouldn't normally consider.
Notice how the word captures both physical distance and emotional intensity. Just as your fingertips are the most remote parts of your body, the extremity of a situation is when things have gone as far as they can go. A lost explorer at the extremity of exhaustion has reached the absolute limit of their endurance, just as the extremity of a peninsula juts out as far as the land extends into the sea.