Dilations and Scale Factor

1
Dilationsand Scale Factor
2
Comparisons of Transformations

• The flips, turns, and rotations are all forms of
  rigid motion.
• A figure that is mapped by a rigid transformation
  does not change in either shape or size (although
  it may change in orientation).
• In a size transformation, sometimes called a
  dilation, a figure keeps its shape but changes
  its size.

3
Dilations

• If the figure increases in size, the
  transformation is an expansion.
• If the figure shrinks in size, the transformation
  is a contraction.
• In either case, the preimage and its image are
  similar. Similar figures have the same shape,
  but a different size.

4
Application - Photography
5
Applications

• Diagrams, blueprints, maps, etc are also commonly
  found in varying sizes.
• Computers allow you to change the size of letters
  without changing its shape.

6
Size Transformations

• ? Size transformations have a
• center and a scale factor.
• If the scale factor is greater than 1, the
  transformation is an expansion. If the scale
  factor is less than 1, it is a contraction.

7
8.1 Dilations and Scale Factors
Draw a dilation on a coordinate plane.
The endpoints of the image are (1, 3) and (2, 1).
8
Example

• Suppose point O is the center of the size
  transformation and the scale factor is 2. Find
  the image of the triangle.

9
What do we know?

• The scale factor of 2 indicates the
  transformation is an expansion.
• The distance from O to must be twice the
  distance from O to A.
• Also O 2OB and O 2OC.
• 3) O, A, and are collinear. O, B, and are
  collinear. O, C, and are collinear.

10
Plan

• Count squares. From O to A is up 7 and right 2.
  So is up another 7 and right 2.
• This insures that O, A, and are collinear and
  that the distance from O to is twice the
  distance from O to A.
• Slope may be used in a similar manner to find the
  other points.

11
Solution
12
Example

• Suppose point O is the center of the size
  transformation and the scale factor is -1. Find
  the image of the triangle.

13
Transformation - Contraction

• Find the image of the quadrilateral under a size
  transformation of
• (or 21) with center at 0.

14
Try It

• By counting squares

15
Solution
16
Homework 502/ 7-24