解:如图,以$B$为原点,分别以$BC,$$AB$所在直线为$x$轴、$y$轴,
建立平面直角坐标系$. $过点$D$作$DH\perp BC,$垂足为$H$
则易得$AD = BH = 1,$$AB = DH$
∵在$Rt\triangle DHC$中,$∠DCH = 30°,$∴$DH=\frac 12CD = 1$
∴由勾股定理,得$CH=\sqrt {CD^2-DH^2}=\sqrt 3$
∴$AB = 1,$$BC = BH + CH = 1+\sqrt 3$
∴$A(0,$$1),$$B(0,$$0),$$C(1+\sqrt 3,$$0),$$D(1,$$1)$