Defining Dilations
Defining dilations is a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 2: Transformations, where a dilation changes the size of a figure by a scale factor k with respect to a fixed center of dilation. All points on the original figure map to corresponding points such that the distance from the center to each image point is k times the distance from the center to the original point. Lines from the center through original vertices always pass through the corresponding image vertices.
Key Concepts
A dilation is a transformation that changes the size of a figure by a scale factor $k$ with respect to a fixed point called the center of dilation .
All points on the original figure are mapped to corresponding points on the image such that the distance from the center to each image point is $k$ times the distance from the center to the corresponding original point.
Common Questions
What is a dilation in geometry?
A dilation is a transformation that changes the size of a figure by a scale factor k from a fixed center point. Each image point is k times as far from the center as its corresponding original point.
What is the center of dilation?
The center of dilation is the fixed reference point from which all distances are measured and scaled. Lines connecting corresponding original and image points all pass through the center of dilation.
How is a dilation different from a translation or rotation?
Translations and rotations are rigid motions that preserve size. A dilation changes size while preserving shape. The image is similar (not congruent) to the original unless k equals 1.
What textbook covers defining dilations in Grade 7?
Big Ideas Math Advanced 2, Chapter 2: Transformations covers the definition of dilation including center of dilation, scale factor, and the distance relationship.