Why did Rick Riordan chose to put the Medusa scene in that particular chapter/placement in Lightning Thief?

For example, someone else did a report on Percy, Annabeth, and Tyson, and Clarisse slaying the Hydra in The Sea of Monsters. He said that Riordan chose to put it in the 2nd book, and the 2nd important thing that happened in the book, because slaying the Hydra was Hercules' second labor. Just looking for a little explanation, btw there could be several different answers to this question, there is not just one correct answer.