# How do you find scale factor?

##### 1 Answer
Feb 3, 2016

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 $f \ne 0$.

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
$| O A \frac{|}{|} O A ' | = | f |$
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.