This is an S O S:

The above is the version of OS X Yosemite - showing on my *iMac when clicked on System Preferences, and as result I have not been able to make the Mini DisplayPort to HDMI Adapter to LG Plasma TV Screen to work.
My *iMac is -
iMac (27-inch, Late 2009) | iMac10,1 (10.10.1) | MB952XX/A |
Running OS X Yosemite
When the above image is compared with the following image below, there is definitely something missing and it’s probably affecting the Mini DisplayPort to HDMI Adapter to work in my connection.

Questions:
How can I make my iMac to have the above AirPlay mirroring or Arrangement?
Is there other ways I can make the connection to work?