Authorities say the 44-year-old assaulted the victim several times at a home in Point Pleasant and that the assaults had occurred for more than a year.
But they won't discuss how Bordenabe knew the youth, who is now 16, saying they want to protect the victim's identity.
Bordenabe is a math teacher and girl's soccer coach at Hudson County Prep, a school in Jersey City that operates as part of the county's Schools of Technology district.
Officials there were notified of Bordenabe's arrest, but did not comment on it.
