A dilation is a transformation 
, with center O and a scale factor of k that is not zero, that maps O to itself and any other point P to P'.
The center O is a fixed point, P' is the image of P, points O, P and P' are on the same line.
In a dilation of the scale factor, k is mapping the original figure to the image in such a way that the
distances from O to the vertices of the image are k times the distances
from O to the original figure. Also the size of the image are k times the
size of the original figure.
Thus for a dilation using the rule
results in the distance of the image form O being twice the distance of the original point from O.
Therefore, it can be observed that the scale factor of the dilation, k, is 2.
In a dilation of
Thus for a dilation using the rule
Therefore, it can be observed that the scale factor of the dilation, k, is 2.