Scale factor is the ratio between the length of any linear component of the image to the length of its corresponding original component.

Scaling is a transformation of objects on a plane that is characterized by
(a) the center of scaling ##O##
(b) scaling factor ##f!=0##.

If these two characteristics are know, the image of any point ##A## is constructed by connecting point ##O## to point ##A## and finding on that line such a point ##A’## that
##|OA|/|OA’| = |f|##
Point ##A’## lies on the same side from center ##O## as point ##A## if ##f>0## and on the opposite side form center ##O## for ##f<0##.

Scaling proportionally changes all the lengths of straight segments, preserves the angles and, in particular, preserves parallelism and perpendicularity between straight lines.

A concept of similarity is completely based on scaling. See UNIZOR menu items Geometry – Similarity many details, theorems and problems.