Focus spot

When take a picture by pressing the shutter button halfway down so that it sets the focus on the desired object, then move the camera so as to set the desired composition, I notice that after I take the picture the red dot showing where focus was set on shows focus to have been set on a different spot than I had selected when I pushed shutter button 1/2 way down.  

Why is this?

I have it set to one shot by the way, not synchro.