The way I understand how a touch screen works, is the glass is electrically conductive which sends a charge signal to the cable attached at the top, behind the ear piece.
Now since you have a crack, I assume the crack goes from edge to edge on the corner of the glass, correct?
If this crack goes all the way through the thickness of the glass, the electrical charge won't be able to travel to the part that's connected to the phone and read your gesture
So the majority of your screen will work, however the smaller area has lost connectivity. Think of it as an island breaking off the mainland.
I hope I've made sense. :3