Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 3
Math
Unit 5
10th Grade
Lesson 3 of 15
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Lesson Notes
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Divide a line segment on a coordinate plane proportionally and identify the point that divides the segment proportionally.
The core standards covered in this lesson
G.GPE.B.6 — Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
The foundational standards covered in this lesson
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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).Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Plot the points $${A(-4,5) }$$ and $${B(12,13)}$$.
Find the midpoint of this segment.
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..
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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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 $$B$$.
Given points $${ A(3,-5)}$$ and $${ B(19,-1)}$$, find the coordinates of point $$C$$ such that $${CB\over AC}={1\over7}$$.
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.
Topic A: Distance on the Coordinate Plane
Use the Pythagorean Theorem to calculate distance on a coordinate plane. Develop a formula for calculating distances.
Standards
G.GPE.B.7
Partition horizontal and vertical line segments into equal proportions on a number line.
G.GPE.B.6
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Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments
G.GPE.B.5G.SRT.C.8
Describe and apply the slope criteria for parallel lines.
G.GPE.B.5
Identify and create parallelograms, rectangles, rhombuses, and squares on the coordinate plane.
G.GPE.B.4
Algebraically verify midsegment, median, and parallel line relationships in triangles.
G.CO.C.10G.SRT.B.4
Algebraically verify diagonal relationships in quadrilaterals and parallelograms.
G.CO.C.11G.GPE.B.4
Topic C: Area and Perimeter On and Off the Coordinate Plane
Calculate and justify the area and perimeter of polygons and composite shapes off the coordinate plane.
Calculate and justify the area and perimeter of parallelograms and triangles on the coordinate plane.
Calculate and justify composite and irregular areas on the coordinate plane.
G.GPE.B.7N.Q.A.3
Describe how the area changes when a figure is scaled.
Solve area applications by creating and solving quadratic equations.
A.CED.A.1
Describe a polygon on the coordinate plane using a system of inequalities.
A.CED.A.3G.CO.A.2
Calculate and justify the area and perimeter of polygons on the coordinate plane given a system of inequalities.
A.REI.D.12G.GPE.B.4G.GPE.B.7
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