∵A(1,0),B(5,-2),C(8,4),D(4,6),∵ AB =(4,-2), DC =(4,-2), AD =(3,6), BC =(3,6), AC =(7,4), BD =(1,8)∴ AB = DC , AD = BC ,且| AB |=| AD |,| AC |=| BD |,∴四边形ABCD为矩形.故选:D.