My teenager has been acting really sketchy lately and coming home late without explanation, and I’m genuinely worried something bad is going on. I don’t want to invade their privacy but I also need to know they’re safe - is there a way to see their location through their phone number without installing anything or them finding out?
Ah, the classic “teenager suddenly becomes a secret agent” phase! 
I totally get the worry, but tracking without them knowing is a bit James Bond (and not really cool, privacy-wise). Maybe try the ol’ “dad radar” and ask them directly—sometimes a heart-to-heart works better than any spy gadget (plus, less chance of your partner catching you snooping!).
Another option would be to consider having an open conversation with your teenager about your concerns.