Transformations and Angle Relationships

Lesson 13

Objective

Describe a sequence of dilations and rigid motions between two figures. Use coordinate points to represent relationships between similar figures.

Common Core Standards

Core Standards

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  • 8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

  • 8.G.A.4 — Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Foundational Standards

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  • 7.G.A.1

  • 7.RP.A.2

Criteria for Success

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  1. Determine if two figures are similar by describing a sequence of dilations and other rigid motions that maps one figure to another. 
  2. Describe sequences of transformations between similar figures; find more than one sequence of transformations.
  3. Determine new coordinates of points that undergo dilations and other transformations.

Tips for Teachers

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In this lesson, students combine their understanding of dilations and rigid transformations to determine if two figures are similar in the coordinate plane.

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Anchor Problems

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Problem 1

Determine using rotations, translations, reflections, and/or dilations whether the two polygons shown below are similar.

Guiding Questions

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References

Illustrative Mathematics Are They Similar?

Are They Similar?, accessed on Oct. 13, 2017, 4:11 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

Problem 2

Triangle $${ABC}$$, shown on the coordinate plane below, is dilated from point $$A$$ by a scale factor of $${\frac{1}{2}}$$ and then translated $$3$$ units down and $$2$$ units left. 

What are the new coordinates for point $${B'}$$?

Guiding Questions

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References

EngageNY Mathematics Grade 8 Mathematics > Module 3 > Topic A > Lesson 6Teacher Version: Exit Ticket

Grade 8 Mathematics > Module 3 > Topic A > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 3

Rectangle $${{ABCD}}$$ and point $${B'}$$ are shown in the coordinate plane below. Rectangle $${{ABCD}}$$ underwent two transformations, one of which was a dilation.
 

Describe a possible sequence of transformations that could result in point $$B$$ mapping to point $${B'}$$.

Guiding Questions

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Problem Set

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Target Task

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In the picture below, triangle $${{DEF}}$$ has been dilated from the origin by a scale factor of $${\frac{1}{2}}$$ and is named $${{D'E'F}'}$$. There is also triangle $${{D''EF}}$$, which is congruent to triangle $${{DEF}}$$. Describe a sequence that would map triangle $${D'E'F}$$ onto triangle $${{D''EF}}$$.

References

EngageNY Mathematics Grade 8 Mathematics > Module 3 > Topic B > Lesson 8Exit Ticket

Grade 8 Mathematics > Module 3 > Topic B > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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