Let the centre be at O(p,q). Distance x of A from O is 0-p=-p and distance y of A from O is 0-q=-q.
Now apply the dilation of 2, so distance x of A' from O is -2p and distance y is -2q.
We add these displacements to O(p,q) to find the new coords of A': p+(-2p)=-p and q+(-2q)=-q.
So we have A'(-p,-q)=(5,5). Therefore p=-5 and q=-5 and the centre is O(-5,-5), coincident with vertex C and answer choice D.