JERUSALEM — Muhammad Abu Khdeir, 16, spent his last hours before being abducted, beaten and most likely burned to death in one of his favorite places, doing some of his favorite things.

Until about 1 a.m. Wednesday, a close cousin said, Muhammad was at the recreation center named for his respected, expansive Palestinian family in the ancient section of the East Jerusalem neighborhood of Shuafat, impressing friends with his defensive prowess at the foosball table and watching World Cup matches on a flat-screen television he recently helped install.

“He came in with a Coke, he’s got to carry a bottle of Coca-Cola all the time,” said the cousin, Mohsen Abu Khdeir, a 40-year-old chiropractor who runs the center, called a “hoash” in Arabic. “He was a comedian kind of guy, always joking. He’s the dynamo. He’s the motor of the hoash.”

It was only three hours after Dr. Abu Khdeir dropped off Muhammad at home that he saw a Facebook post saying that the boy had been snatched from the street in what is widely suspected to have been an act of revenge by Jews for last month’s kidnapping and killing of three Israeli teenagers. On Saturday, the Palestinian attorney general said that an autopsy had found soot in Muhammad’s lungs, suggesting that he had been burned alive before his charred body was found in a forest.