Final answer:
The x and y coordinates for the center of dilation depend on the specific details of the transformation, which aren't provided in the question. For displacement vector calculations, the differences in x and y coordinates are found by subtracting the initial point's coordinates from the final point's coordinates.
Step-by-step explanation:
The x coordinate and the y coordinate for the center of dilation in a coordinate system are the values that represent the fixed point from which all other points are scaled in a dilation transformation. To find these coordinates, one needs specific information about the transformation because the center can be any point in the plane. For example, if a problem defines that the center of dilation is at the origin, then the x coordinate would be 0 and the y coordinate would also be 0. Without specific details of the dilation or the pre-image and image coordinates, we cannot determine the exact x and y coordinates of the center of dilation.
If a displacement vector is being calculated, as indicated in the part of the question, then the x and y components of the displacement (Dx and Dy) can be found by subtracting the coordinates of the initial point from the coordinates of the final point. If point b is at (6.0, 1.6) and point e is at (2.0, 4.5), then the displacement vector is found by completing the subtraction: Dx = 2.0 - 6.0 = -4.0, and Dy = 4.5 - 1.6 = 2.9.