extreme point vs extremity

extreme point and extremity both are nouns.

Word	Noun	Adjective	Verb	Adverb
extreme point	Yes	No	No	No
extremity	Yes	No	No	No

As nouns, extremity is a hypernym of extreme point; that is, extremity is a word with a broader meaning than extreme point:

extreme point (noun)	extremity (noun)
the point located farthest from the middle of something	an external body part that projects from the body
	that part of a limb that is farthest from the torso
	the outermost or farthest region or point
	the greatest or utmost degree
	an extreme condition or state (especially of adversity or disease)