Question

the center of dilation is at point ( , )

Explanation:

Step1: Recall Dilation Center

The center of dilation is the point through which all lines connecting corresponding vertices of the pre - image and image pass.

Step2: Find Intersection Point

We look at the lines connecting the corresponding points of the two triangles (pre - image and image). By observing the graph, we can see that the lines connecting the corresponding vertices intersect at the point \(I\) (or the point with coordinates \((-8,0)\)). To verify, we can check the lines: for example, the line connecting the top vertex of the smaller triangle and the top vertex of the larger triangle, the line connecting the bottom vertex of the smaller triangle and the bottom vertex of the larger triangle, and the line connecting the other corresponding vertices all pass through \((-8,0)\).

Answer:

\((-8,0)\)