Also, to MGibson, there are a lot of factors from the OP that we’re filling in with our own brains, so a lot of disagreement can arise.
If I live in the woods, the chances of a warning shot harming someone can be significantly less than if I live in a close residential neighborhood, so this comes down to how well you know your own house, and ect.
Also, the type of pistol isn’t specified (And I’m actually presuming it’s a pistol and not, say, a shotgun.). The difference between a .44 magnum and a .22 would be a factor. A .44 can tear someone’s leg completely apart.
The exact level of darkness isn’t specified, but I’m presuming if you can see well enough to think someone has a knife, you can see their legs. I’d shoot for what I can see.
The scenario may be altered in my mind by the foreknowledge that it’s a 14 year old, which I wouldn’t have.
Also, ‘morning after’ legalities probably won’t change your mind if this actually happens. If your level of fear is high enough to shoot to kill, you probably will even if you’ll go to jail the next day for it. If you feel a tinge of half-heartedness(And as I said it might not be in me if it weren’t for the foreknowledge.) you may shoot someone in the leg.
If someone had broken into my home and was armed with a knife to my knowledge, I might shoot for the legs. ‘Morning after’ legalities aside, I might still do it.
This also presumes they are standing still(Or a non-threatening movement). If they are moving towards me, I would probably go for the center of mass. If it was too dark to discern anything but the figure, aside from identifying that I do indeed know they are there, I would probably shoot for the center of mass. If I think they may have a gun, I would probably shoot for the center of mass.
I would also, from the get go, assume that they intend to do me or my family some sort of bodily harm, because at my house you can tell when we’re home. I’m in the ‘bible belt’, so anyone breaking into a home when they know people are home can usually assume a firearm is also present and the owner will use it. In fact, I don’t know anybody who doesn’t own a gun. I know this is not the case in many areas.
The OP is sort of General Purpose.