Sometimes, especially for duplicate special, you need to freeze transformations for it to work probably.
And you don't have to duplicate it over the origin. Using a negative value for scale will invert the object (in the relevant axis) over the pivot.

You need to make sure your border edge is on a single plane(parallel to one of the axis) - In your case all the vertices on the border edge need to have 0 value in either x, y(unlikely) or z.
Then place the pivot anywhere on that plane(the origin will do for most cases), freeze transformations and duplicate with a negative value.
Hope this helps,
Benny