I was able to find the center of enlargement $(3,0)$ and the scale factor $-\frac{1}{2}$. I tried to write the rule for the dilation and I had $(x,y) \rightarrow (-\frac{1}{2}x+\frac{9}{2}, \frac{1}{2}y)$. But seems so off. I can't figure out how to write the dilation rule.
In two dimensions, scaling around a point is $$\left\lbrace ~ \begin{aligned} x^\prime &= x_0 + s ( x - x_0 ) \\ y^\prime &= y_0 + s ( y - y_0 ) \\ \end{aligned} \right.$$ where $(x_0, y_0)$ is the center, $(x, y)$ is a point in the original coordinate system, $s$ is the scale factor, and $(x^\prime, y^\prime)$ is the point in the scaled coordinate system (image). This should apply to each of your point pairs ($A$ and $A^\prime$, $B$ and $B^\prime$, and $C$ and $C^\prime$).
If the center is $C = (3,0)$, then $A - C = (3,-1)$ and $A^\prime - C = (-3,2)$; that does not seem like a scale factor of half to me; it looks to be an integer.
(In other words, you do have the correct center, but your scale factor is wrong.)