Verify experimentally the properties of dilations given by a center and a scale factor:
  1. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
  2. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Similarity, Right Triangles, & Trigonometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand similarity in terms of similarity transformations. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes


  • Item Type(s): This benchmark may be assessed using: MS item(s)

  • Assessment Limits :
    Items may use line segments of a geometric figure.

    The center of dilation and scale factor must be given.

  • Calculator :


  • Clarification :
    When dilating a line that does not pass through the center of dilation,
    students will verify that the dilated line is parallel.

    When dilating a line that passes through the center of dilation,
    students will verify that the line is unchanged.

    When dilating a line segment, students will verify that the dilated line
    segment is longer or shorter with respect to the scale factor.

  • Stimulus Attributes :
    Items may give the student a figure or its dilation, center, and scale
    and ask the student to verify the properties of dilation.

    Items may be set in a real-world or mathematical context.

  • Response Attributes :



  • Test Item #: Sample Item 1
  • Question:

    Quadrilateral MATH is shown.

    Quadrilateral MATH is dilated by a scale factor of 2.5 centered at (1,1) to create quadrilateral M'A'T'H'. Select all the statements that are true about the dilation.

  • Difficulty: N/A
  • Type: MS: Multiselect