Definition: A scale factor is the number by which every length of a figure is multiplied to make an enlarged or reduced copy of it.
What is a scale factor?
When you resize a figure so the shape stays the same, every length is multiplied by the same number, the scale factor. A factor above 1 enlarges, a factor between 0 and 1 shrinks, and 1 leaves the size unchanged.
How do you find it?
Divide a length in the new figure by the matching length in the original. A rectangle 6 cm by 10 cm becomes 15 cm by 25 cm. Then 15 / 6 = 2.5 and 25 / 10 = 2.5, so the scale factor is 2.5.
What happens to the area?
Lengths scale by k, but area scales by k squared. Here the area goes from 60 to 375, and 60 x 2.52 = 60 x 6.25 = 375. Perimeter scales by k.
Where is it used?
Maps, models, and blueprints. A model car at scale factor 1/24 has every length 24 times smaller than the real car.
What is a common mistake?
Mixing the direction. Scale factor from new to original is the reciprocal, 1/2.5 = 0.4.