DynamicModule[{dragging = False, start}, EventHandler[
Graphics[
{EdgeForm@Gray,
FaceForm@None, GraphicsComplex[
Dynamic@If[dragging,
{start, MousePosition["Graphics"]},
{ImageScaled@{-0.1, -0.1}, ImageScaled@{-0.1, -0.1}}
],
{Rectangle[1, 2], Line@{1, 2}}
]
},
Frame -> True,
PlotRange -> 1
],
{
"MouseDown" :> (dragging = True; start = MousePosition["Graphics"]),
"MouseUp" :> (dragging = False)
}
]
]