As the end of Chapter Nine explores, the scene where Ender kills the snake and then sees Peter's bloody reflection in the mirror that he gazes into suggests strongly that Ender has the potential to turn into a Peter-like figure who kills without moral scruples and enjoys the feeling of destruction and ending the lives of others. Note what Ender thinks when he reflects on what he saw in the computer screen:
He kept remembering how it felt to kill the snake, grinding it in, the way he tore the ear off that boy, the way he destroyed Stilson, the way he broke Bernard's arm. And then to stand up, holding the corpse of his enemy, and find Peter's face looking out at him from the mirror. This game knows too much about me. This game tells filthy lies. I am not Peter. I don't have murder in my heart.
The short and simple sentences at the end suggest a matter-of-fact, determined tone of voice that reveals Ender's inner thoughts and feelings in response to the rather disturbing image of himself that he sees. Yet what is more worrying is the way that in the next paragraph Ender is left with the nagging fear and suspicion that he may actually be a killer like his brother, and that he is slowly but surely being fashioned into precisely the killer that is needed to triumph in the bugger wars and save humanity. The reflection in the mirror therefore does not tell lies, and ironically, Ender is completely correct with his doubts, as he turns into the biggest killer of all, but only without his knowledge.
Peter's reflection represents how Ender sees Peter in himself. In fact, Ender cries that he has become too much like Peter. In actuality, this is what Graff wants to an extent. Peter was too violent and ruthless to become a commander. Ender is too just and docile. But its easier to bring out just the right amount of ruthlessness in him than to curb Peter's tendencies. The reflection shows how much Ender wishes to not be like Peter against Graff's wishes.