Remember that the horizontal and vertical flip buttons use the "transform origin" that's shown with the rotate handles to set the "mirror line".

So:
* Draw a background square
* Draw a squiggly shape on one side
* In the Selector tool, make sure the squiggle is selected and then click it again to show the rotate handles and the transform origin (the "target" handle in the middle)
* Make sure magnetic snapping is turned on and drag the transform origin until it snaps to the middle of the background square
* Clone the squiggle and click flip horizontally (and/or flip vertically)

The cloned squiggle will then be /exactly/ opposite the original w.r.t. the background.

Phil