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Moses and Elijah
Matthew 17:1 or Mark 9:2
On the Mount of Transfiguration, Jesus was "transfigured," meaning that he was seen by the Apostles Peter, James and John in his glorified form, bright as the sun in blazingly white clothes. In this form, he spoke with Moses and Elijah, who also appeared there with Jesus. See Luke 9:28-36.
Jesus prayed on the Mount of Olives, specifically in the Garden of Gethsemane on the night before his crucifixion.
It is believed to be the traditional place of the Transfiguration of Jesus in front of Peter, James, and his brother John.
The Transfiguration of Jesus is recorded in the Synoptic Gospels (Matthew 17:1-9, Mark 9:2-8, Luke 9:28-36), which, as you mentioned in your question, involved the appearance of Elijah and Moses with Jesus. As for where it occured, Christian tradition says it took place on Mount Tabor. More recent scholars suggest that the "high mountain" mentioned in the passage could have been Mount Hermon or Mount Nebo.
To the garden of Gethsemene and the mount of transfiguration.
Because Peter, James and John had witnessed the transfiguration at the mount and Jesus wanted to keep it a secret.
Church of the Holy Transfiguration of Christ-on-the-Mount was created in 1891.
Jesus and Moses were not contemporaries, although Moses did appear with Elijah to Jesus on the Mount of Transfiguration. Jesus did give respect and credibility to Moses' writings and referred to the fact that Moses spoke about Him in His writings.
Jesus took a few disciples to a mountain call Mount of Transfiguration. Where the two prophets of old prophet Elijah and prophet Moses were seen by the disciples.
None. Only Moses appeared to Jesus and three of his disciples on the mount of transfiguration: And after six days Jesus taketh with him Peter, and James, and John, and leadeth them up into an high mountain apart by themselves: and he was transfigured before them. And his raiment became shining, exceeding white as snow; so as no fuller on earth can white them. And there appeared unto them Elias with Moses: and they were talking with Jesus. (Mark 9.2-4)