Q: Is it possible to get airplay on a mid 2010 macbook pro

Nope.

Requirements for using AirPlay

If you go to Apple menu > System Preferences, click Displays, and don't see the option to "Show mirroring options in the menu bar when available," your Mac doesn't meet these requirements.

Minimum requirements if your Mac and Apple TV are on the same network:

• Apple TV (2nd generation or later) with the latest Apple TV software
• For mirroring your display or extending your desktop, any of the following Mac computers with OS X Mountain Lion v10.8 or later:
  • iMac (Mid 2011 or later)
  • Mac mini (Mid 2011 or later)
  • MacBook (Early 2015 or later)
  • MacBook Air (Mid 2011 or later)
  • MacBook Pro (Early 2011 or later)
  • Mac Pro (Late 2013 or later)

Use AirPlay to display video from your Mac on an HDTV - Apple Support

About AirPlay and Airplay Mirroring

AirPlay Mirroring requires a second-generation Apple TV or later, and is supported on the following Mac models: iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer). For non-qualifying Macs you can try using Air Parrot.

Several Apple Articles Regarding AirPlay

Apple TV (2nd and 3rd gen)- How to use AirPlay Mirroring

How to set up and configure AirPort Express for AirPlay and iTunes

iTunes- Troubleshooting AirPlay and AirPlay Mirroring

iTunes- Using AirPlay

Apple TV (2nd and 3rd gen)- Understanding AirPlay settings

About AirPlay Mirroring in OS X Mountain Lion

iTunes 10- About playing music with AirPlay

Troubleshooting AirPlay and AirPlay Mirroring

Using AirPlay

Thanks to the $15 Beamer, AirPlay streaming is still possible on Macs  that do not support Airplay and mirroring.

Other solutions are the Air Parrot, StreamToMe, and AirServer.