My sister’s boyfriend tried to kill her, and now he can’t be found. Can facebook be used to track his location?
Yes, if he log on Facebook frequently. Police can track his geolocation by locating his IP Address.
Yes, if he logs into Facebook a record will be made of his IP address and probably his geolocation as well.
This is a job for the authorities, as Jan said. If this guy really tried to kill someone, you don't want to be doing your own weekend work trying to find him through the Internet. Please let the police know immediately.
There is a multitude of factors going into whether it is possible to track someone or not regardless of it being via website like Facebook, an app or the phone itself.
Provide the police with all relevant information e.g. FB profile, known phone numbers, email addresses, twitter account, etc. and they will do their best as far as technically possible.