A-Level student Jeshma Raithatha was raped and murdered at random as she walked home from school, police said.
Jeshma was stabbed to death
Jeshma, 17, is thought to have been grabbed by a stranger on a secluded footpath in Sudbury Hill, west London, at about 1500 BST on 16 May.
At first police thought she died six days later, but now believe she was murdered on the day she disappeared.
They are still looking for a man who lived near Jeshma but has gone missing from his home.
His and two other houses in Dimmock Drive are being searched by officers, but police have refused to identify the man.
Jeshma's partially clothed body was dumped in dense undergrowth at the back of a leisure centre. She had been raped and stabbed three times through the heart.
Detectives initially thought she had been killed elsewhere, but now think she was grabbed as she walked along the footpath and forced into a "wooded den". Her body lay undiscovered for eight days.
Jeshma's aunt, speaking to BBC News, said on Tuesday: "There has been a lot of speculation recently, a lot of it wrong, but a random attack is something we had been thinking about.
"We just now hope they catch her killer.
"Jeshma was a young, smart funny, bubbly girl with everything to look forward to. All that has now been snatched away."
Jeshma was found in a wooded area not far from her home
Details of Jeshma's last movements were outlined by police who are hoping more witnesses will come forward.
She had been to school to study for her exams and left at 1300 BST, catching the bus to Wembley High Road, where she went shopping in Primark and TownCity.
She then got the 92 bus back to Sudbury Hill, where she arrived at about 1500 BST.
As she headed home, she took a footpath through the wooded area where she was killed. The area is still being searched for clues.
Detectives plan to release CCTV footage of Jeshma shopping on Wembley High Road.
Her mother said Jeshma, who would have turned 18 days after her disappearance, was committed to her studies and wanted to study music and media at university.
She rarely went out at night on her own and was usually picked up from school, but as an A-Level student was not expected in school all day and had left early.
Det Ch Supt Andy Murphy said: "She did not have a complicated life in any way, shape or form. It appears she was the victim of a random attack."