DANVERS, Mass. — She had a bright smile, a penchant for pink and an admitted overenthusiasm for the subjects she taught. The lanky boy was just a decade younger, new to the school, with a pleasant manner but little to say.

Sometime on their last day at the school together Tuesday, prosecutors say, teacher Colleen Ritzer and 14-year-old student Philip Chism crossed paths, and he killed her.

Ritzer’s body was later found in the woods behind Danvers High School, where she taught and Chism attended classes. And on Wednesday, Chism was being held without bail after being arraigned on a murder charge.

Ryan Kelleher, who had Ritzer for algebra and played soccer with Chism, said none of it made sense.

“From what I know about him and seeing him every day, it just doesn’t add up that he would do such a thing, unless this was all an act to fool somebody,” said Kelleher, 17.

Officials haven’t released a cause of death or discussed a motive in the killing. A court filing said Ritzer and Chism knew each other from the high school, but it didn’t elaborate.

Blood found in a second-floor school bathroom helped lead investigators to Ritzer’s body, after she was reported missing Tuesday, Essex District Attorney Jonathan Blodgett said.

Investigators said in court documents that the arrest was made based on statements by the suspect, evidence from school surveillance cameras and corroborating evidence in multiple places.

Chism’s family and attorney did not comment Wednesday.

Chism had moved to Massachusetts from Tennessee before the start of the school year and was a top scorer on the school’s junior varsity soccer team, said Kyle Cahill, a junior who also plays soccer.

He said the team had been wondering where Chism was when he skipped a team dinner Tuesday night.

“We’re all just a family. It just amazes me really,” Cahill said. “He wasn’t violent at all. He was really the opposite of aggressive.”

The Boston Red Sox held a moment of silence for Ritzer on Wednesday at Fenway Park before Game 1 of the World Series.

Hundreds of people later turned out for a candlelight vigil at the school parking lot, many wearing pink sweatshirts, bows or T-shirts in tribute to Ritzer and her favorite color.