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Place a piece of painter's tape on the wall roughly where you want the object to be. Then use the measuring tape to measure the height of the exact spot. Mark it on the painter's tape using a pencil. The painter's tape will help keep the plaster from cracking when you drill into it. Use a drill bit that is narrower than the width of the screws you are using. For instance, if you are using screws that are 0.25 inches (0.64 cm) wide, use a drill bit that is 3⁄16 inch (0.48 cm). Drive the bit into the wall at the spot you marked. Work carefully, holding the drill at a right angle to the wall. Plaster is hard, so you will feel some resistance. That resistance may increase if the drill enters the lathe (the wooden support that holds up the plaster). Switch to a screwdriver attachment on your drill. Drive a screw almost all of the way in. Leave a bit of distance between the screw head and the wall surface. Wrap one end of a wire tightly around the screw head. Attach the other end to the hook or support on the object you want to hang. Adjust the wire length until the object is at the height you want.  Some objects (like many picture frames) will have a hole in the back that you can set directly on the screw to hold it in place. Use a level to fine-tune the placement of your object.
Mark the spot where you want to hang the object. Pre-drill a hole. Drive a screw into the spot you marked. Hang your object.