She was found dead in her third-floor apartment in Congress Heights, naked from the waist down and with her hands tied behind her back. Police said that Rachel Cox, 43, had been sexually assaulted and stabbed several times.

The day was Jan. 1, 1984, the same year scientists developed a technique to use DNA to identify people but long before unique genetic sequences became as common as fingerprints in criminal investigations. At the crime scene, authorities collected bodily fluid and a cigarette butt discarded under a table and stored them for another day.

That day finally came.

In January, nearly 30 years after Cox was killed, detectives submitted the fluid and cigarette butt for DNA testing and got hits on both. D.C. police said Tuesday that modern-day testing revealed that genetic material from the fluid matched a profile from a sex offender who had raped a 10-year-old girl months after Cox was killed and just blocks from where she was attacked. It was the first break in the unsolved, apparently random killing.

On Tuesday, police arrested a warehouse laborer in Woodbridge, Va., and charged him with felony murder. Joe Anthony Barber, 55, is being held until his next court hearing, on Nov. 15.

Cases like this have become common in recent years, with DNA used to arrest and convict people in what had once seemed impossible-to-solve crimes as well as to exonerate others sent to prison on what had appeared to be airtight evidence.

Collectively, DNA databases in Maryland, Virginia and the District hold more than 600,000 genetic codes, most taken from convicted felons.

The U.S. Supreme Court, in a 5 to 4 decision in June, allowed Maryland to take DNA samples from some arrestees, ruling the procedure no different than fingerprinting someone being booked on criminal charges but not yet convicted.

Maryland’s DNA database, for example, has 107,000 samples, nearly 2,600 added this year alone. Last year, authorities reported 45 matches between crime scene evidence and someone in the database. That led to nine arrests and six convictions.

The number of people in the District’s database could not be learned Thursday. Samples are taken from felons before they’re sent to federal prisons across the United States.

D.C. officials said there have been 73 DNA hits this year but could not say how many have led to arrests.

Max Houck, director of the D.C. Department of Forensic Sciences, said that making an arrest in a 30-year-old case remains fairly noteworthy, although he pointed to reports last month that scientists had mapped the genome of a 4-year-old who died in Russia 24,000 years ago.

“Solving a 30-year-old homicide probably shouldn’t amaze us,” he said.

Houck said it wasn’t too long ago that a DNA sample “had to be the size of a quarter to get a reading. Now we’re able to test amounts we can’t even see — down to 10 or 12 skin cells.”

The DNA samples obtained at the scene of Cox’s killing were tested by an outside firm, using federal grant money, before the new lab was opened.

Cox’s daughter said earlier this week that relatives were excited by news of an arrest but did not want to speak publicly.

D.C. police said the attack on Cox, which occurred before 6:30 a.m. New Year’s Day 1984, appeared to be random. Detectives at the time had little evidence, and the cigarette butt and swabs taken from the victim were virtually useless with the technology available at the time.

But the items were saved, and on Jan. 16, they were submitted to Bode Technology Group of Virginia. A genetic profile from the swabs matched a profile of the suspect, who was on the Virginia State Police’s sex-offense registry. The butt belonged to someone else, according to court documents.

Police obtained another, more current DNA sample from the suspect, and that also was a match, according to the court documents.