Curriculum  /  Math  /  10th Grade  /  Unit 1: Constructions, Proof, and Rigid Motion  /  Lesson 14

Constructions, Proof, and Rigid Motion

Lesson 14

Math

Unit 1

10th Grade

Lesson 14 of 19

Objective

Perform reflections on a coordinate plane across axes and other defined lines. Identify characteristics and an algebraic rule for the reflection.

Common Core Standards

Core Standards

  • G.CO.A.2 — Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
  • G.CO.A.4 — Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
  • G.CO.A.5 — Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
  • G.CO.B.6 — Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Foundational Standards

  • 8.G.A.1
  • 8.G.A.3

Criteria for Success

  1. Describe that rigid motions describe ways you can move a figure either on or off a coordinate plane without changing size, shape, angles, or relationship between any of the parts. 
  2. Describe reflections as a rigid motion of individual points across a line of reflection. To define a reflection, all that is needed is a line of reflection. 
  3. Describe that a line of reflection can be in any orientation (horizontal, vertical, or diagonal) and that it can be on a figure, outside a figure, intersect with a figure, or be inside a geometric figure. 
  4. Perform a reflection on a coordinate plane by reflecting points over any given line (not just an axis or y=x).
  5. Use an algebraic rule to show the reflection of a figure over an axis or the line y=x. Describe where the general rule is derived from. 
  6. Understand that there are an infinite number of fixed points with a reflection, but all fixed points are on the line of reflection. 
  7. Describe the relationship between the distance of each point on the original figure and the reflected figure to the line of reflection.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

  • Reflect $${\overline{AC}}$$ over the $$x$$-axis
  • Reflect $${\overline{A'C'}}$$ over the $$y$$-axis

Guiding Questions

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

Problem 2

Reflect $${\angle DAC}$$ over the line $${y=x}$$.

Guiding Questions

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

Problem 3

Given the set of points below, what is the line of reflection for the image?

Image: $${E' (-2,1)}$$, $${F' (-3,3)}$$

Pre-image: $${E (1,-2)}$$, $${F (3,-3)}$$

Guiding Questions

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

Target Task

5-10 minutes

Line segment $${\overline{DF}}$$ is shown below. Reflect this over the x-axis.

  • What is the line of reflection? 
  • Describe the reflection.
  • What features are “preserved” in a reflection?  
  • What is the algebraic rule for the reflection?

Additional Practice

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

  • Include problems where students need to: 
    • Find the line of reflection, citing half the distance between corresponding points on the two line segments. 
    • Reflect an angle given the line of reflection. 
    • Identify an incorrect reflection. 
    • Describe a reflection with algebraic notation (if an axis or y=x /y=-x line).
    • Reflect a line segment given the line of reflection. 
    • Translate angles and segments as review.
  • Include matching cards with lines of reflection, original figures, and final figures. This Mathematics Assessment Project lesson will be used in the next unit, but can be used as a reference for style to create matching cards for this lesson.
  • CPALMS Angle Transformations — Only ask questions about translations and reflections, not rotations. This resource does a good job of focusing on the distance preservation of rigid motions.
  • CPALMS Segment Transformations — Only ask questions about translations and reflections, not rotations. This resource does a good job of focusing on the distance and angle preservation of rigid motions.

Next

Use construction and patty paper to reflect a figure not on the coordinate plane. Describe the properties of a reflection.

Lesson 15
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Constructions of Basic Geometric Figures

Topic B: Justification and Proof of Angle Measure

Topic C: Translations of Points, Line Segments, and Angles, and Parallel Line Relationships

Topic D: Reflections and Rotations of Points, Line Segments, and Angles

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free