Connecting a Mac Mini to an iMac 2009
How to connect aMac Mini to a iMac 2009
If the 2009 iMac is 27" it can be used a a display for a Mac mini (even a 2020 Mac mini, despite what Apple say, because the 2009 iMac is not using Thunderbolt).
Use your iMac as a display with target display mode - Apple Support
You will need a USB-C to Mini DisplayPort cable, such as: