Unless you have a helper or a very small area to repair, affix a firring strip or similar-sized piece of trim to the wall under the ceiling, running side to side the width of the new piece going in. This will bear the weight of the replacement piece while you are securing it with screws. Pic 1.

Mark an arrow on the wall (or trim piece, as shown) and another arrow on the existing ceiling opposite, both pointing to the center of the middle ceiling rafter. Pic 2.

These arrows are your points of reference for drawing a line across the new piece to indicate where the drywall screws will go to secure the new piece to the dead center of the middle rafter.