Draw a picture! A mirror on the wall, and a little lady standing in front of it.
First of all, how do you see yourself in the mirror? Light bounces off your body, and then bounces off the mirror into your eyes.
So let's think about this. In order to see your feet, there must be enough mirror so that light will be able to bounce off the wall and into your eyes. Also, because of snell's law, we know that the angle of incidence = angle of reflection. So if the light originates at your feet, where must it bounce off the wall so that it can get into your eyes?
Since Incidence = Reflection and assuming you're standing perfectly straight, the vertical distance traveled before the light hits the mirror must be the same as the vertical distance traveled after it hits the wall. Thus, it must bounce right in the half way point between the floor and the top of your head. thus, mirror = h/2