Polygons and Algebraic Relationships

Lesson 14

Math

Unit 5

10th Grade

Lesson 14 of 15

Objective


Describe a polygon on the coordinate plane using a system of inequalities.

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).
  • A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Foundational Standards

  • A.CED.A.2
  • 6.G.A.3

Criteria for Success


  1. Write a system of inequalities to describe a polygon on the coordinate plane. 
  2. Using a set of vertices, write a system of inequalities to describe the polygon on the coordinate plane. 
  3. After a transformation, write a system of inequalities to describe a polygon on the coordinate plane.
  4. Describe how a transformation effects the system of inequalities that describes a polygon on the coordinate plane.

Tips for Teachers


  • Students may need to review how to write a system of inequalities before they can fully access this lesson. It is recommended to spend time outside of class building this specific skill.
  • This lesson is an extension of the G-CO.2 standard, which is important because it prepares students to access F-BF.3 by beginning to identify effects of transformations on equations.
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Anchor Problems


Problem 1

Given the quadrilateral below:

  1. Identify the vertices.
  2. Write a system of inequalities to describe this quadrilateral.
  3. Is this quadrilateral a parallelogram? A rectangle? A rhombus? A square? Explain your reasoning. 
  4. Translate the polygon right 6 units; write a new system of inequalities to describe this translated polygon.

Guiding Questions

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Problem 2

Given $${(0,0)}$$, $${(1,3)}$$, and $${(2,1)}$$,

  1. Draw the triangular region on the coordinate plane.
  2. Write a system of inequalities to describe this region.
  3. Is this triangle a right triangle? Explain your reasoning.
  4. Find the area and perimeter of this triangle.

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 4 > Topic A > Lesson 2Example 2

Geometry > Module 4 > Topic A > Lesson 2 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 Fishtank Learning, Inc.

Target Task


Given the trapezoidal region,

a. Write the system of inequalities describing the region.

b. Translate the region to the right 3 units and down 2 units. Write the system of inequalities describing the translated region.

References

EngageNY Mathematics Geometry > Module 4 > Topic A > Lesson 2Problem Set, Question #4

Geometry > Module 4 > Topic A > Lesson 2 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..

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 the original polygon is transformed and write a new system of inequalities.
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Lesson 13

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Lesson 15

Lesson Map

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

Topic A: Distance on the Coordinate Plane

Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments

Topic C: Area and Perimeter On and Off the Coordinate Plane

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