To find the scale factor, you need to compare the corresponding sides of two similar figures or objects. The method depends on whether you are scaling up (making the figure larger) or scaling down (making the figure smaller):
- For scaling up (from smaller to larger), calculate the scale factor by dividing the larger measurement by the smaller measurement. This will give a ratio greater than 1.
- For scaling down (from larger to smaller), calculate the scale factor by dividing the smaller measurement by the larger measurement. This will give a ratio less than 1.
In formula terms:
Scale Factor=Length of new figureLength of original figure\text{Scale Factor}=\frac{\text{Length of new figure}}{\text{Length of original figure}}Scale Factor=Length of original figureLength of new figure
Make sure to use the lengths of corresponding sides. The scale factor shows how many times larger or smaller the new figure's dimensions are compared to the original's. For example, if a side in the original figure is 12 cm and the corresponding side in the new figure is 36 cm, the scale factor going up is 3612=3\frac{36}{12}=31236=3. If scaling down from 36 cm to 12 cm, the scale factor is 1236=13\frac{12}{36}=\frac{1}{3}3612=31. This principle applies to all corresponding dimensions of similar shapes. The scale factor is consistent across all such dimensions.
