Gift Makau, 18, was found dead in Tshing location on Friday.
She had been raped and strangled with wire and a shoelace. A running hose had been forced into her mouth.
Her cousin, Lucky Gaorongwe, said yesterday that her murder was particularly shocking because the suspect was well known in the area.
"She [Gift] had never been abused or heckled in the community," her cousin said.
"She was a cool girl who was never violent. She enjoyed playing and refereeing soccer games in the neighbourhood."
He said her family, who knew she was a lesbian, was devastated.
"Her mother is not coping at all, but we’re trying – and people have been supportive."
Makau, the youngest of three children, is to be buried on Saturday.
The police said yesterday that a man will appear in the Ventersdorp Magistrate’s Court today.
Jabu Pereira, director of the lesbian, gay, bisexual, transgender and intersex human rights organisation Iranti-org, said: "These heinous crimes have to end.
"Our government must invest in public education programmes aimed at changing public attitudes."