The bodies of three young Virginia women were found early Saturday evening lying side by side on the floor of a trailer used as a sales office for a housing development on the edge of Dale City, Prince William County police disclosed yesterday.

Police said that each of the women had been shot at least once in the back of the head with a handgun and that some of their personal property had been stolen. Police said they have no suspects and have established no motive for the slayings.

Two of the victims were described by police and acquaintances as close friends who had gone to the Dale City area Saturday afternoon to look at new homes for sale there.

One of the women, 25-year-old Sharon Lake, already lived in Dale City; her friend Debra Warner Frank, 23, of Alexandria was looking for a home in the area, according to a local realtor.

The third victim was identified as Karen Rose Scarbrough, a 17-year-old Fredericksburg. Va., woman who had graduated from high school one week ago and was working temporarily as a receptionist at the trailer, police and other sources said.

The bodies were discovered face down on the trailer floor at 6:55 p.m. Saturday by a sales manager for Ryland Homes, who had gone to the trailer to use a telephone, police said. Ryland plans to build about 100 new homes in a large cleared area near the sales office trailer, sources said.

Police said there were no signs of struggle within the trailer. They said it appeared that the women had laid down on the floor voluntarily.

The victims were identified as Lake, a Prince William County elementary school teacher who lived on Maverick Court in Dale City; Frank, who loved on Richmond Highway in Alexandria and who worked for a McLean consulting firm, and Scarbrough, a recent graduate of Stafford High School, who until recently lived in a trailer park with her parents 10 miles north of Frederickburg, and moved into the city of Fredericksburg three months ago.

Frank and Lake were described by an associate as close friends, whose husbands both worked at the Pentagon in the Air Force Data Services Center. A spokesman for the Air Force said Frank's husband, Sandy, is a civilian mathematician and that Lake's husband, Capt. Calvin K. Lake, is a computer program analyst.

The Lakes had moved to the Washington area from Louisiana earlier this year and had purchased a home in Dale City, according to the associate, who asked not to be identified. The Franks had been looking for a home in the Northern Virginia area for about a month, the associate said.

According to police, Mrs. Frank met Mrs. Lake at about 4 p.m. Saturday, went to a supermarket in the Forrestdale section of Dale City and then drove to a sales office of Hylton Enterprises Inc. about a mile from the scene of the shootings.

At the Hylton sales office, the women talked to John A. Dunn, a sales manager who had sold the Lakes their home. Dunn said yesterday Mrs. Lake told him she was showing her friend some homes. The two women took some Hylton brochures and left the office, Dunn said.

Police said yesterday that they believe the two women arrived at the Ryland Homes trailer at about 4:30 p.m. The trailer is on a dead end at the western end of Dale Boulevard, adjacent to the land that has been cleared for the Ryland housing development. The trailer was about 100 yards from another housing development - built by Hylton - which is now almost fully occupied. Across from the trailer is a dense wooded area.

Resident of the housing development said they heard nothing unusual on Saturday.

Dunn said the two women's husbands became concerned when their wives did not rejoin them as planned. The men drove to the Dale City area, where they were met by police and informed of the shooting, according to Dunn who said he had spoken to a relative of the dead women. Police refused to confirm Dunn's information.

At about 6:55 p.m., Ryland's sales manager, John McCauley, arrived at the trailer, went inside to use the telephone, discovered the bodies of the three women just inside the entrance to the trailer and called police.

Meanwhile, a source said, Scarbrough's mother had arrived at the sales office and was sitting in her car waiting to give her daughter a ride home from work. When police arrived, the mother was informed of the shootings, the source said.

Police said Sharon Lake and Debra Frank were dead at the scene of the incident. Scarbrough was transported to the Potomac Hospital in Woodbridge where she was pronounced dead.

The shootings apparently occurred between 4:30 p.m. and 5:40 p.m. police said.

Friends said the Lakes had been married about five years and the Franks about a year. Neither couple had children, friends said.

"Both couples were extremely well liked and both very happy," one associate said.

Scarbrough was described by friends as a quiet woman who liked to stay at home.

"I don't think she's done anything wrong to anybody," one friend said.