The Prince George's County government has agreed to pay $10,000 to the mother of a 17-year-old youth who was shot to death three years ago by a police officer investigating a burglary in Palmer Park.

The out-of-court settlement of the lawsuit filed against the county by Virginia Washington marks the first time in the past three years that the county has agreed to compensate the family of a victim fatally shot by police.

During that three-year period, there have been three incidents of white officers fatally shooting blacks, incidents that exacerbated existing tensions between the police and residents of predominantly black communities in Prince George's.

County Attorney James C. Chapin said yesterday that the county and Washington's lawyer had agreed to the terms last Thursday. The case had been scheduled to go to trial in federal court in Baltimore on Tuesday.

"We agreed to terms based on nuisance value," Chapin said. "We're not admitting in any way that the officer did anything wrong. We just thought it would cost less, win or lose, to settle out of court."

Washington filed suit against both the county and officer Frank M. Cohee last July, alleging that her son's civil rights had been violated by the shooting.

The $1 million lawsuit was filed last July, after Maryland's Court of Special Appeals ruled that the Prince George's County executive had no right to order the police department to bring officer Cohee before a police board for a disciplinary hearing.

Earlier, a county grand jury had declined to bring any charges against the officer in connection with the Washington shooting.

Michael A. Washington of 8129 Sherrill St., Palmer Park, was killed on the morning of April 30, 1975, moments after Cohee and another officer were called to investigate a burglary in progress in Palmer Park.

According to Cohee, he entered the house and, hearing a sound in a living room closet, hid behind a couch. Cohee said he saw a hand come out of the closed holding "a shiny object," and fired one shot, low into the closet.

Washington was found, crouched down, shot fatally in the chest with a butcher knife lying next to him.Cohee was placed on administrative leave for three months but was exonerated both criminally and administratively and returned to duty by Police Chief John W. Rhoads.