Scaling factor

Definition

A scaling factor is a number by which all dimensions of an object are multiplied to achieve a proportional enlargement or reduction. It maintains the geometric similarity between the original and scaled objects.

5 Must Know Facts For Your Next Test

1. A scaling factor greater than 1 enlarges the object, while a factor less than 1 reduces it.
2. In similar triangles, corresponding sides are proportional based on the scaling factor.
3. The ratios of corresponding side lengths in similar triangles are equal to the scaling factor.
4. Scaling factors do not affect the shape of an object, only its size.
5. If two triangles are similar, their areas are proportional to the square of their scaling factor.

Review Questions

• What happens to a triangle when it is multiplied by a scaling factor greater than 1?
• How does a scaling factor relate to the corresponding sides in similar triangles?
• Why does a scaling factor not change the shape of an object?

Related terms

Similar Triangles: Triangles that have identical shapes but different sizes due to proportional side lengths.

Proportionality: The relationship where two ratios or fractions are equal.

Geometric Similarity: When two shapes have the same form but may differ in size.