MA19.GDA.26

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.26

Verify experimentally the properties of dilations given by a center and a scale factor.

Unpacked Content

Knowledge

Students know:
  • Methods for finding the length of line segments (both in a coordinate plane and through measurement).
  • Dilations may be performed on polygons by drawing lines through the center of dilation and each vertex of the polygon then marking off a line segment changed from the original by the scale factor.

Skills

Students are able to:
  • Accurately create a new image from a center of dilation, a scale factor, and an image.
  • Accurately find the length of line segments and ratios of line segments.
  • Communicate with logical reasoning a conjecture of generalization from experimental results.

Understanding

Students understand that:
  • A dilation uses a center and line segments through vertex points to create an image which is similar to the original image but in a ratio specified by the scale factor.
  • The ratio of the line segment formed from the center of dilation to a vertex in the new image and the corresponding vertex in the original image is equal to the scale factor.

Vocabulary

  • Dilations
  • Center
  • Scale factor
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