Where is Ender in the computer game? What does he see in the mirror after he defeats the snake? Why?Ender's Game Chapter 8

At Battle School, Ender plays an open-ended adventure game
that seems to have no clear point/ultimate goal. Ender is often frustrated by the game,
and finds himself stuck at a particular point. He tries various methods to beat the
level. He eventually manages to defeat a character (the giant) through violence. The
violent act fueled by frustration and rage, and is somewhat out of character for Ender
-- or, at least, out of what he hopes is his character. He fears the dark, impulsive
side of himself (the same side that, earlier in the novel, led him to brutally beat a
bully), but it is that side that allows him to advance to the next level. His character
climbs a beanstalk (like in Jack and the Beanstalk), and he explores the giant's palace.
Eventually, he defeats a snake (again, though violence), and finds himself face to face
with a mirror. At this point, Ender is so closely identified with the character in the
game that he feels as if he is actually having this experience himself. It is that
closeness that makes the mirror's reflection more disturbing. In the mirror, Ender sees
not his own face but the face of his brother, Peter. Peter is cold, manipulative,
violent, and cruel, and the mirror's reflection is a representation of Ender's greatest
fear: that in the end, he will be just like his brother.