A dilation represents a transformation 
, centered at point O with a scale factor of k, which cannot be zero. This transformation keeps O fixed while transforming any other point P into its image P'. Points O, P, and P' are collinear.
In a dilation of
, the scale factor 
maps the original figure to its transformed image in such a way that the distances from O to points of the image are half the distances from O to the original figure. Consequently, the image's size is also half that of the original figure.
Thus, <span>If represents the dilation of △ABC, then the properties of the image △A'B'C'</span> are:
<span>AB is parallel to A'B'.
The distance from A' to the origin is half that from A to the origin.</span>
In a dilation of
Thus, <span>If
<span>AB is parallel to A'B'.
The distance from A' to the origin is half that from A to the origin.</span>