Verses with the word point in the New Testament (3 verses):

Mark 5:23
And besought him greatly, saying, My little daughter lieth at the point of death: I pray thee, come and lay thy hands on her, that she may be healed; and she shall live.

John 4:47
When he heard that Jesus was come out of Judaea into Galilee, he went unto him, and besought him that he would come down, and heal his son: for he was at the point of death.

James 2:10
For whosoever shall keep the whole law, and yet offend in one point, he is guilty of all.