Question

How do you find scale factor?

Answer 1

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

Explanation:

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.