Defining the Scale Factor (k): Enlargements and Reductions
Defining the scale factor k and understanding enlargements versus reductions is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 2: Transformations. If k is greater than 1, the dilation is an enlargement; if 0 is less than k which is less than 1, it is a reduction; and if k equals 1, the image is congruent to the original. For example, scale factor k equals 0.5 creates an image half the size of the original.
Key Concepts
For a dilation with scale factor $k$: If $k 1$, the dilation is an enlargement (image is larger than original) If $0 < k < 1$, the dilation is a reduction (image is smaller than original) If $k = 1$, the image is congruent to the original figure.
Common Questions
What is a scale factor in math?
A scale factor k is the ratio used in a dilation that determines how much the figure grows or shrinks. If k is greater than 1 the image is larger (enlargement), if k is between 0 and 1 the image is smaller (reduction).
What is the difference between an enlargement and a reduction in dilation?
An enlargement has a scale factor k greater than 1 and produces an image larger than the original. A reduction has scale factor between 0 and 1 and produces a smaller image.
What happens when the scale factor is exactly 1?
When k equals 1, each side length is multiplied by 1, so the image is exactly the same size as the original. The transformation creates a congruent figure.
What textbook covers scale factors for dilations in Grade 7?
Big Ideas Math Advanced 2, Chapter 2: Transformations covers scale factors and how to identify enlargements versus reductions.