How do you find scale factor?

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.