Final answer:
Dilation is a transformation that does not preserve the length of the sides of a quadrilateral.
Step-by-step explanation:
The rule that does NOT preserve the length of the sides of the quadrilateral is Option 4: Dilation.
Dilation is a transformation that stretches or shrinks a figure without altering its shape. It multiplies the coordinates of each point by a scaling factor, which can be greater than 1 or less than 1. As a result, the lengths of the sides of the quadrilateral will change.