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How show Locator point and its image under a function?


The following code displays a fixed point and its image under a 
specified function f:

   f[{x_,y_}]:={2x+1,y+2}
   Module[{pt = {-1, 0.5}},
      Row[{
        Framed@Graphics[Point[pt], PlotRange -> 5],
        Framed@Graphics[Point[f[pt]], PlotRange -> 5]
      }]
    ]

Now I want to have the point in the left-hand graphic to be dynamic, 
controlled by a Locator, and to have its changed image under the 
function to be shown in the right-hand graphic.

The idea is something like the following (WRONG!) code:

   DynamicModule[{pts={{0,0}}},
     Row[{
       LocatorPane[Dynamic[pts],Graphics[{},PlotRange->5]],
       Graphics[Dynamic[f/@pts],PlotRange->5]
     }]
   ]

That code produces error messages, "1 is not a Graphics primitive or 
directive", "2 is not a Graphics primitive or directive".

How can it actually be done?

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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