Home > Lessons > Dilations
Search | Updated August 5th, 2018
    In this section of MATHguide, you will learn about dilations. Here are the topics within this page:

    Similar Figures -- a topic covered in another section -- can be described by the mathematics of dilations.

    Dilations have these features:

  • They have a center of dilation.
  • They have a scale factor.
  • There is the original figure and it's image figure.

    When we refer to the original figure, of say a triangle, we call the original figure △ABC. We call the image figure △A'B'C'. The second triangle is pronounced, "triangle A-prime, B-prime, C-prime."

    A characteristic called scale factor informs us of the relationship between the original figure and its image. The scale factor is typically called the k-value.

    When the k-value is 0 < k < 1 [greater than zero but less than one], the image figure is smaller than the original figure. When the k-value is k > 1 [greater than one], the image figure is greater than the original figure. This information is encapsulated within the diagram that follows.

    The video below will demonstrate exactly how dilations work.

      ideo: Dilations

    Here is a quiz that can be used to test your understanding of dilations.

      uiz: Dilations

    This is a lesson that uses scale factors. After this lesson, students will be ready to move on to Areas and Lengths of Similar Figures and Volumes and Lengths of Similar Solids (see the related lessons section below).

      ctivity: Scale Model of the Solar System
      ctivity: Planet Information
      ctivity: Scale Solar System (Excel)

    View these related lessons.

      esson: Reducing Fractions
      esson: Geometry Proofs
      esson: Proportions
      esson: Similar Figures
      esson: Areas and Lengths of Similar Figures
      esson: Volumes and Lengths of Similar Solids