Extended display with 2010 macbook pro

You can do that with the MDP to HDMI adapter and a HDMI cable, no additional hardware required.
But know, that TVs are not meant to be used as computer displays, as they are softer and bigger with a low resolution (eg. 30" with 1920 x 1080 pixel, compared to a 30" computer display with 2560 x 1600 pixel).

 

Yup, that will certainly work.

Quick question: do you want your TV to play the sound, too? If not, I would actually recommend using VGA if your TV has it.

Over the years, I've found that using a TV as a computer monitor is a bit more user friendly when the computer sees the TV as a monitor instead of a TV. Resolution options are a little funkier when the computer recognizes a TV. And you might have to toy with Overscan issues, too.
The digital to digital concept is a nice one, but VGA seems to be plenty capable these days of 1 to 1 pixel mapping, and the computer seeing the TV as just a regular LCD monitor makes life easier in my mind.
Though, if you want sound, getting video and audio over one cable is handy.

As for the low resolution of TVs, it's true, the pixel density of TVs is generally much less than a laptop screen. Think, the 13" MBP has a 1280x800 resolution, and most HD content is still in 720p, which is roughly 1366x768 (same resolution as the 11" MBA!). So, for a 37"/42"/47"+ TV, that's some pretty big dots. At best a TV is 1920x1080, and there are 15" laptops out there with 1920x1200 resolutions.
That said, an external screen is an external screen, and it will be increased screen real estate regardless.

Cheers!