This ratio shows us the scale factor
1) Suppose we have an original polygon that has the following length: 4" and this polygon has been dilated with a scale factor k=2.
2) Then the polygon will have their lengths equal to 8" and that statement refers to the ratio:
Hence, this ratio shows us the scale factor used in this Dilation. Note that since it was greater than 1, it means an enlargement, lesser than 1: the dilated figure has been shrunk.