Unit A: Geometry

Chapter 2: Transformations

A transformation is the movement of an object by changing its position, size, and/or shape. There are four different types of transformations that have been studied in Chapter 2.

  • A dilation is the change in the size of a shape or object.
  • A translation is the horizontal and/or vertical movement of a shape or object.
  • A reflection is a transformation that creates a mirror image of the original shape or object.
  • A rotation is the movement of a shape or object around a fixed point.

Graphic designers use transformations when creating logos or page designs. When preparing the layout for a project, the graphic designer may need to translate (move), rotate (turn), reflect (flip), or dilate (enlarge or reduce) an image or text.

In the logo, the comma, , is transformed to produce other images.



The original comma, 0, is translated to the right and down to produce image 1 .

Graphic designers may need to apply more than one transformation to create an image.

Image 2 is created from the original comma by applying three transformations:
  1. a dilation (enlargement)
  2. a rotation to the left (counterclockwise)
  3. a translation to the left and down

Image 3 is also produced by applying three transformations:
  1. a dilation (reduction)
  2. a reflection (or 180° rotation)
  3. a translation to the left and down

By the end of this lesson, you will be able to

  • draw the image of a 2D shape that results from a combination of two successive transformations
    • translation
    • reflection
    • rotation
    • dilation
  • identify two transformations that have been applied to a shape or object
  • create, analyze, and describe transformations, using translations, rotations, and reflections in all four quadrants of a coordinate grid
  • solve problems involving transformations