A triangle has vertices at (1,1), (1,2), and (3,2). It is dilated by a scale factor of 3 with the origin as the center of dilation to form a similar triangle. What are the coordinates of the vertices of the image?
A:(4,1), (4,2), (6,2)
B:(1,4), (1,5), (3,5)
C:(4,4), (4,6), (6,5)
D:(3,3), (3,6), (9,6)
