A 23-year-old clerk-typist for the city's housing department was found beaten and strangled Wednesday in her apartment on a quiet, tree-lined street in Northwest Washington, police reported yesterday.

The body of the woman, Glendora Mackenhimer, was discovered by her mother and sister, who became concerned after they had been unable to reach her during the day. They went to her first-floor apartment in the building where all three lived at 5610 Colorado Ave. NW.

Her partially unclothed body was found on the floor of the living room, said her sister. Teresa. According to the medical examiner's office, the victim died of "multiple injuries." Officials declined to be more specific.

The slaying shocked neighbors on the quiet block of well-kept three-story apartment buildings and single family homes.

"I can't remember when anything like this ever happened around here," said an elderly man, who said he has been living on the block for about 15 years.

Jean Mackenhimer, the mother of the slain woman who lives in an apartment near the victim's, said she last talked with Glendora about 1 a.m. Tuesday in what she said was a routine conversation.

"It's a sad thing," her mother said yesterday. "She was such a friendly person. She loved people. . . . I have been living here for 12 years and we haven't had anything like this before, especially not in this building."

Police said they had neither a motive nor a suspect in the slaying. There was no sign of forced entry to the apartment nor did anything appear stolen, police said.

A team of homicide detectives has been assigned around-the-clock to work on the case, said Capt. Jimmy Wilson, head of the homicide division.

Henry E. Brooks, an assistant supervisor for the field office of the city's Department of Housing and Community Development, said Glendora Mackenhimer called in sick on Tuesday and did not report to work on Wednesday. She worked at 23 M St. NE.

The victim's mother said she and her daughter Teresa went to Glendora's apartment about 6 p.m. Wednesday.

Jean Mackenhimer said "Candy" -- the victim's nickname -- was born in Washington, but grew up in Rocky Mount, Va. She graduated from high school and moved to Washington after graduation.

She had been working for the city's housing department since May 10, 1976, her supervisor said.

"She was a very outgoing person," said Tom Jones, an assistant director at the housing field office. "She was very attractive and seemed happy all the time."

The victim's mother said her daughter did fashion-modeling as a hobby. "She always wanted to be a stewardess," Jean Mackenhimer said. However, she said her daughter never achieved that ambition and decided to go into modeling.

Jean Mackenhimer said her daughter had held a yard sale outside the apartment building last Saturday. "She was pretty excited about it and had planned to make it an annual affair," said her mother, who said Saturday's yard sale was the second one she had held.

As family members and friends gathered in Jean Mackenhimer's neatly furnished apartment yesterday, homicide detectives were across the hall looking for clues in the victim's apartment.