In chapter 10, Percy's reaction towards his conflicts is to fight.
We learn in the chapter that Annabeth and Grover are accompanying Percy on his quest. Before they leave, Chiron gives Percy the weapon Anaklusmos (or "Riptide"). Riptide, as Percy prefers to call it, is actually a powerful, celestial sword disguised as a pen.
When Percy, Annabeth, and Grover board the bus, a nasty surprise awaits them. Mrs. Dodds and two other old ladies are there. In reality, the three old women are the Furies: Greek goddesses of vengeance.
To protect Percy, Annabeth gives Percy her Yankees cap (a present from her mother, Athena), which makes him invisible to everyone. Initially, Percy refuses to leave his friends; but, as the Furies reveal their true selves, he is forced to accept Annabeth's help.
Instead of getting off the bus, however, Percy makes his way to the front of the bus. There, the invisible Percy tries to take over the wheel from the bus driver. The bus veers to the side, while both the bus driver and Percy wrestle for the wheel. Eventually, Percy manages to press on the emergency brake. As a result, the bus veers off the road and crashes into some trees.
Everyone gets off the bus, except for the Furies, Grover, Percy, and Annabeth. As for Percy, he unsheaths Riptide and uses it to engage in an epic fight with the Furies. Annabeth and Grover fight by his side.
In the end, Percy manages to dispatch two of the Furies with Riptide. Mrs. Dodds, however, remains relatively unscathed. She eventually becomes so desperate that she blows up the bus in an attempt to kill them.
Percy, Grover, and Annabeth manage to flee the bus before it explodes, but they find that they have to get further away. With the two Furies dispatched and Mrs. Dodds on the run, it's only a matter of time before reinforcements come to attack the three young friends.
In all, Percy decides to stand and fight, despite the dangers he encounters.