When barium sulphate reacts with copper sulphate, a double displacement reaction takes place. The products of this reaction are barium sulphate and copper sulphate. The reaction can be represented as follows:

$$BaSO_4(s) + CuSO_4(aq) → BaSO_4(s) + CuSO_4(aq)$$

In this reaction, the sulphate ions from the barium sulphate and the copper ions from the copper sulphate exchange places, resulting in the formation of barium sulphate and copper sulphate. Barium sulphate is a white, insoluble solid, while copper sulphate is a blue, soluble solid.