The slot in the bracket on the top of that derailleur that you've overlaid would go underneath the rear wheel axle nut on a regular bike. The slot in the bracket slides over the axle. Other types screw into a threaded hole in the drop-out itself.
It's important that your derailleur placement matches this as closely as possible. It's been designed to function with this in mind. Locate it any more than a few mm away from this ideal and it'll not be able to influence the chain's passage over the sprockets.
So. it is a fairly straightforward job to provide a bracket which will provide a mounting point for the derailleur. However ... the derailleur (that's a very poor drawing of a very old example which predates indexed gears) jockey wheels will sit directly underneath the sprockets. Unfortunately there's a dirty great frame tube directly underneath the sprockets.
I think that you've bought the wrong trike. if you wanted super-low fixed gears you've bought the right one, but if you want a range of gears you should probably accept that this trike is not compatible with such a set up. And either take this back to the shop (if you think they've sold you the wrong thing) or sell it and buy something which suits you.
As it happens I am an expert in the area of provision of bike for people with disabilities. We sell new and refurbished, to individuals mainly, but also large fleets of adapted bikes to schools and local authorities. We see a lot of these trikes on our travels - usually old knackered ones in schools - because at one time this was one of the few disabilty trikes available in the UK. Things have moved on substantially since this trike was designed. But it has remained resolutely unchanged in design since its conception. I'd be interested to know how much one of these things costs new.
I'd have sold you one of these:
http://www.getcycling.org.uk/details.php?id=674&c=194
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