Answer:
The property that must be preserved under this sequence of transformations is distance.
When a sequence of transformations consists of translations, dilations, and rotations, the distances between points remain the same. In this case, the initial translation, dilation, and final translation may change the size, orientation, and position of the figure, but the distances between points remain constant.
Translations move all points in the same direction by the same amount without changing their distances from each other.
Dilations change the size of the figure but preserve the ratios of distances between points. So, although the figure may become larger or smaller, the distances between points remain proportional.
Rotations also preserve distances. They rotate the figure around a fixed point, but the distances between points remain unchanged.
Therefore, under this sequence of transformations, the property that is preserved is distance.