To determine the center of dilation, we need to find the point that is the same distance from each corresponding pair of points in both the pre-image and the image. This point is where all lines drawn from corresponding points of the pre-image and image intersect.

Let's follow these steps to find the center of dilation in the image:

1. The points in the pre-image are labeled $A, B, C$ and in the image as $A', B', C'$.
2. Draw lines through corresponding points $A$ to $A'$, $B$ to $B'$, and $C$ to $C'$.
3. The point where all three lines intersect is the center of dilation.

From observing the graph, the lines drawn from the corresponding points all intersect at the origin, $(0, 0)$. Therefore, the center of dilation is at the point $(0, 0)$.

Would you like a detailed explanation or have any questions?

Here are 5 related questions to explore further:

1. What is the scale factor of the dilation in this transformation?
2. How can you determine if a dilation is an enlargement or a reduction?
3. How does the center of dilation affect the image size and position?
4. Can you have a center of dilation outside of the shape itself?
5. How do you apply the dilation formula to find the coordinates of a transformed point?

Tip: Always check whether the transformation is enlarging or shrinking the figure by comparing the lengths of corresponding sides.