Polygons and Algebraic Relationships

Lesson 3

Math

Unit 5

10th Grade

Lesson 3 of 15

Objective


Divide a line segment on a coordinate plane proportionally and identify the point that divides the segment proportionally.

Common Core Standards


Core Standards

  • G.GPE.B.6 — Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Foundational Standards

  • 7.RP.A.2

Criteria for Success


  1. Describe that to divide a directed line (that is not horizontal or vertical), the vertical and horizontal components of the line segment need to be partitioned separately.
  2. Describe that right triangle legs are formed when horizontal and vertical distances are divided in the desired proportion.
  3. Identify the hypotenuse of the partitioned horizontal and vertical distances as one part of the partitioned line segment. 
  4. Describe that by partitioning the vertical and horizontal components in the desired proportion, you will be partitioning the segment itself in that proportion. 
  5. Verify that a line segment is partitioned in the correct proportion by finding the distance between the endpoints of the partition. 
  6. Describe the relationship between the distance formula and the process for partitioning a line segment into a desired proportion. 
  7. Name a coordinate that is a certain proportion away from one of the endpoints. Verify this distance algebraically.

Tips for Teachers


This lesson is an extension of Lesson 2. We are focusing here on the division of a line segment on the coordinate plane rather than the number line (Lesson 2) or using constructions (Unit 3, Lesson 4 and 6). 

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Anchor Problems

25-30 minutes


Problem 1

Plot the points $${A(-4,5) }$$ and $${B(12,13)}$$.

Find the midpoint of this segment.

References

EngageNY Mathematics Geometry > Module 4 > Topic D > Lesson 12Opening Exercise

Geometry > Module 4 > Topic D > Lesson 12 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.

Problem 2

Find the point on the directed line segment from $${C(-2,0) }$$  to $${ D(5,8)}$$ that divides the line segment in the ratio of $${1:3}$$. Show your reasoning. Then, graph the points to show your reasoning using the graph.

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 4 > Topic D > Lesson 12Exercise #2

Geometry > Module 4 > Topic D > Lesson 12 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

5-10 minutes


Problem 1

Given points $${ A(3,-5)}$$ and $${B(19,-1)}$$, find the coordinates of point $$C$$ that sit $${{3\over8}}$$ of the way along $${\overline{AB}}$$, closer to $$A$$ than to $$B$$.

References

EngageNY Mathematics Geometry > Module 4 > Topic D > Lesson 12Exit Ticket, Question #1

Geometry > Module 4 > Topic D > Lesson 12 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 2

Given points $${ A(3,-5)}$$ and $${ B(19,-1)}$$, find the coordinates of point $$C$$  such that $${CB\over AC}={1\over7}$$.

References

EngageNY Mathematics Geometry > Module 4 > Topic D > Lesson 12Exit Ticket, Question #2

Geometry > Module 4 > Topic D > Lesson 12 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.

Next

Algebraically and using the Pythagorean Theorem, determine the slope criteria for perpendicular lines.

Lesson 4
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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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