Well done Luke and Daniel from year 9 together with Nicholas and Luke from year 7 of Clevedon Community School who sent in the following solution.
The locus of corner D will be a circle with a radius equal to AD, whose centre is A. The locus of the point Y will be a circle with a radius equal to AD, and a centre on AB one third of the way along from A to B.
Can you see the reason for this? The locus of Y is a circle. If you imagine a line joining Y to the centre Z of this circle then DYZA is a parallelogram so ZY = AD and AZ=DY.