WASHINGTON (AP) _ A 12-year-old girl in New York who was among the first to be sued by the record industry for sharing music over the Internet is off the hook after her mother agreed Tuesday to pay $2,000 to settle the lawsuit, apologizing and admitting that her daughter’s actions violated U.S. copyright laws. The hurried settlement involving Brianna LaHara, an honors student, was the first announced one day after the Recording Industry Association of America filed 261 such lawsuits across the country. Lawyers for the RIAA said Brianna’s mother, Sylvia Torres, contacted them early Tuesday to negotiate. “We understand now that file-sharing the music was illegal,” Torres said in a statement distributed by the recording industry. “You can be sure Brianna won’t be doing it anymore.” Brianna added: “I am sorry for what I have done. I love music and don’t want to hurt the artists I love.” The case against Brianna was a potential minefield for the music industry from a public relations standpoint. The family lives in a city housing project on New York’s Upper West Side, and they said they mistakenly believed they were entitled to download music over the Internet because they had paid $29.99 for software that gives them access to online file-sharing services.