Final answer:
To graph the center of dilation A for triangles P and Q, we analyze the changes in their vertices post-dilation and infer that the center remained unchanged in position during the dilation process.
Step-by-step explanation:
To graph point A, the center of dilation, when triangle P is dilated by a scale factor of 2 to form triangle Q, we need to locate a point that relates the corresponding vertices of the two triangles with the given scale factor.
The vertices of triangle P are (-2, 1), (2, 4), and (2, 1), and after dilation to form triangle Q, the vertices are (-1, -3), (7, 3), and (7, -3), respectively.
Let's consider the relationship between the vertices of triangle P and Q. Vertex P(-2,1) is dilated to become vertex Q(-1,-3).
Following the scale factor of 2, we should expect the vertices of Q to be twice the distance from the center of dilation when compared to their counterparts in P. Similarly, for the other vertices of P which becomes (7,3), and (7,-3) in Q after the dilation.
By examining the changes in coordinate values from P to Q, we observe that the horizontal components (x-values) have a pattern of addition or subtraction, suggesting that the center of dilation lies along the same x-coordinate for these points.
The vertical components (y-values) also show consistent change, hinting that the same will be true for the y-coordinate.
Therefore, after evaluating the distance changes, we conclude that the center of dilation is at point A which will have an unchanged position during the dilation process for any point.