Final answer:
If quadrilateral LMNO and QRST are congruent, the transformations that could have been applied are reflection, rotation, and translation. These transformations preserve size and shape, unlike dilation, which changes the size of a figure.
Step-by-step explanation:
If quadrilateral LMNO and quadrilateral QRST are congruent, it means that one can be obtained from the other through transformations that preserve size and shape. The transformations in question include reflection, rotation, and translation. These are known as rigid motions or isometries, which preserve the distances and angles between points. Dilation, on the other hand, changes the size of the figure, hence cannot be used if the quadrilaterals are congruent.
Reflection is a transformation producing a mirror image of the original figure across a line or plane. Rotation involves turning the figure around a fixed point through a specified angle and direction. Translation slides the figure to a new location without changing its orientation or size. Since all these transformations preserve the size and shape of the original figure, they could be the ones applied to create quadrilateral QRST from LMNO. In the context of this question, dilation is not a possible transformation, as it would alter the size of the quadrilateral