What transformations will produce a similar, but not congruent figure?

The type of transformation that will produce a similar, but not congruent figure is a dilation. 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. The scale factor of a dilation is the factor with which the image increase or decrease from the pre image, it also gives the factor with which the the distances from O to the vertices of the image are more than the distances from O to the original figure. For a scale factor between 0 and 1 the image is a shrinking (i.e. the image is smaller that the original figure) while for a scale factor above 1, the image is an enlargement (i.e. the image is bigger that the original figure).