$$AB:BC=1:3$$

$$=>\frac{AB}{AC}=\frac{1}{4}$$

$$\frac{AD}{AE}=\frac{AB}{AC}=\frac{1}{4}$$

$$\frac{AD}{AE}=\frac{1}{4}$$

$$\frac{8-2}{AE}=\frac{1}{4}=>AE=4\times 6=24$$

Therefore, the x coordinate of C is 2+24=26.

$$\frac{DB}{EC}=\frac{AB}{AC}=\frac{1}{4}$$

$$\frac{DB}{EC}=\frac{1}{4}$$

$$\frac{3}{EC}=\frac{1}{4}=>EC=12$$

Therefore, the y coordinate of C is -4+12=8.

The coordinates of point C is (26,8).