I'm glad your self preservation is leading you here. At 9, fury can erode the difference you think you may enjoy from age, and for her to win a fight is worse than the immediate bodily damage.
I'd escalate hard and swiftly on such behavior. The time for threats is quite literally years past.
The playstion is gone, no arguments. So is the TV and music gear. By "gone", I mean they are in the garage of a friend's house, not just a few days without MTV. Obviously any privilege such as pocket money and trips cease. The family goes on a really healthy diet.
When 2.0 threw such a wobbly before 4th birthday, the posters in his room including the Lunar calendar & St. Shrek, were ceremonially removed.
Was inconsolable.
Message was received 100%. But here, we're beyond that.
This isn't a care situation it's win/lose. Until and unless she realises that being on your side is better than being against you, it's only going to get worse.
Although the advice to "remain calm" is good our kids know the difference between the voice that says "why don't you do this", and "this is what you will do now", and "you are opening a door to a place you really don't want to be".
She isn't picking up on this, perhaps by choice, perhaps because she knows you love her, and limit your response.
I fear you may have been too logical and reasonable.
The next step is an attack on your terms, not a response to an outburst. The less you do at any one time, the more you'll have to do in the long run.
Sit her down, and trash a couple of her CDs.
Open a box with her favourite things in it.
Proceed to destroy them.
She will presumably want you to stop.
Her job is to persuade you that her future conduct will save what's left.
Try to order the items by how she values them.
Start with little things, but almost certainly she will threaten you, and/or strike out. This is to be met with the loss of a seriously more loved item.
Given her conduct you will want a large male friend to help you on this, maybe two. Perferably someone she doesn't know too well, and thus cannot guess how he will react. You want someone that can look "thug" well.
When she has made commitments that you actually believe, the box is taken from the house.
The term here is "hostage". Leave her with school clothes, and some deeply horrible gear. If you have the money pay a trip to ASDA and buy some large Tweenies clothes(embarassing to a 9 yo). Else a charity shop will provide strange smelling "granny" clothes. These are for after school and weekends.
Each week of completely acceptable behaviour brings back a small % of her clothes and privileges.
I haven't said much about the root causes of her behaviour. Can't really bring myself to care at this point. My kids would be met with overwhelming misery at the first incident.
This may sound a little harsh, but this is not refusing to do her homework, this is safety critical for here.
You may choose simply to do the nice clothes/charity shop as a first step. Personally I think the situaiton you describe is beyond that, but you know her.
If this was an isolated lash out in the blind temper of a kid, I'd be talking in terms of a nice quiee chat. Dinner at a restaurant is good for this, make her feel grown up and away from standard environment would make for deeper conversation.
After all this is over, that's good maintenance, but we're not there at all.
There is a non trivial chance that her current path will get you or her hurt. Presumably you are allowing her to strike you with little comeback. Bad lesson for her to learn. The chances of her doing this with someone who will retaliate more viciously is far too high.