A potentiometer can be seen as a complete voltage divider circuit
Below we can see a 10K potentiometer analyzed graphically.
First of all 10 K potentiometer means that Rtotal=R1+R2=10K
Observe that by turning the rotor anticlockwise you decrease the R1 and you increase R2 so you increasing Vout
If we want to divide the Vout into the half then R1=R2=R so we have to put the rotor at the middle.
Notice that if you want to make a stable fixed divider you only have to dimension and add at your circuit the two resistors R1 and R2.
For example if we want a Vout divided by two we have to add two same resistors. In our case below we added two 10K resistors.
Below are the virtual circuits using Fritzing
Download the Fritzing and Dia diagrams from here : VoltageDivider
A video demonstration is posted below :