TRADING PLACES: When Adaptoid hits a single-base character with a close combat attack, after actions resolve Adaptoid and the hit character may be placed in each other's squares.

Obviously you have to be adjacent for this to take affect. So if I roll doubles and knock my opponent away from me , do I still get to trade places?

why would they not? Nothing in the power says that they have to be adjacent.

All it cares is that you hit someone with a Close Combat Attack. That is it.