1. The problem is to understand how to find the scale factor between two similar figures. 2. The scale factor is the ratio of any two corresponding lengths in the two figures. 3. The formula for the scale factor $k$ when you know the lengths of corresponding sides $a$ and $b$ is: $$k = \frac{\text{length in image}}{\text{length in original}} = \frac{b}{a}$$ 4. Important rule: The scale factor is the same for all corresponding sides in similar figures. 5. For example, if one side in the original figure is $5$ units and the corresponding side in the image is $15$ units, then: $$k = \frac{15}{5}$$ 6. Simplify the fraction: $$k = \frac{\cancel{15}}{\cancel{5}} = 3$$ 7. This means the image is scaled by a factor of $3$ compared to the original figure. 8. So, the scale factor tells you how much larger or smaller the image is compared to the original.