Transformations and Angle Relationships

Lesson 5

Objective

Describe sequences of transformations between figures using reflections and translations. Use coordinate points to represent relationships between reflected figures.

Common Core Standards

Core Standards

?

  • 8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.

  • 8.G.A.1.B — Angles are taken to angles of the same measure.

  • 8.G.A.1.C — Parallel lines are taken to parallel lines.

  • 8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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

Criteria for Success

?

  1. Perform a combination of transformations, using translations and reflections, on a figure. 
  2. Describe a sequence of transformations, using translations and reflections, between two figures. 
  3. Understand that reflecting an image across the $$y-$$axis results in the $$x-$$coordinate becoming its opposite value; reflecting an image across the $$x-$$axis results in the $$y-$$coordinate becoming its opposite value. 

Tips for Teachers

?

  • This is the second lesson on reflections. Students start to think about multiple transformations by combining reflections and translations. 
  • Students begin reasoning about coordinate points as they connect to transformations, building up to Lesson 9 where they will tackle challenging problems with all types of transformations.
  • The following materials are useful for this lesson: patty paper (or transparency paper) and graph paper.

Fishtank Plus

Subscribe to Fishtank Plus to unlock access to additional resources for this lesson, including:

  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package

 

Anchor Problems

?

Problem 1

Figure 1 is reflected over the $$y$$-axis to create Figure 2, as shown in the coordinate plane below.

  1. Describe what you notice about the coordinate points of a figure when it is reflected over the $$y$$-axis.
  2. What do you think happens to coordinate points of a figure when it is reflected over the $$x$$-axis?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Triangles $${{ABC}}$$ and $${{PQR}}$$ are shown below in the coordinate plane.

Describe a sequence of transformations that can map $${{ABC}}$$ to $${{PQR}}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

?

With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Examples where students give new coordinate points of figures that are transformed (by a reflection, a translation, or a combination of both)
  • Examples where students perform sequences of reflections and translations in the coordinate plane
  • Examples where students are given two figures and describe the sequence of transformations (reflections, translations, or combinations); explain why the two figures are congruent, similar to Anchor Problem #2
  • Examples of error analysis or incorrectly described sequences

Target Task

?

Below is a picture of a triangle on a coordinate grid:

  1. Draw the reflection of $${\triangle ABC}$$ over the vertical line through $${x=-2}$$. Label the image of $$A$$ as $$A'$$, the image of $$B$$ as $$B'$$, and the image of $$C$$ as $$C'$$.
  2. Draw the reflection of $$\triangle A'B'C'$$ over the vertical line through $${x=2}$$. Label the image of $$A'$$ as $$A''$$, the image of $$B'$$ as $$B''$$, and the image of $$C'$$ as $$C''$$.
  3. What single rigid transformation of the plan will map $${\triangle ABC}$$ to $$\triangle A''B''C''$$? Explain. 

References

Illustrative Mathematics Reflecting Reflections

Reflecting Reflections, accessed on Oct. 13, 2017, 4 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.

Mastery Response

?

Create a free account or sign in to view Mastery Response