Dilation by a scale factor of 2 does not preserve the distance between points.
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Rigid transformation are transformations that preserve the shape and size of a figure. Rigid transformation include rotation, reflection and translation.
Dilation is not a rigid transformation, because it only preserves the shape but not the size.
Hence the transformation that does not preserve distance between points in quadrilateral ABCD is the dilation by a scale factor of 2.
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