Polygons and Algebraic Relationships

Lesson 1

Math

Unit 5

10th Grade

Lesson 1 of 15

Objective


Use the Pythagorean Theorem to calculate distance on a coordinate plane. Develop a formula for calculating distances.

Common Core Standards


Core Standards

  • G.GPE.B.7 — Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • 8.G.B.8

Criteria for Success


  1. Describe that the distance on a horizontal line segment is the change in $${x-}$$coordinates, whereas the distance on a vertical line segment is the change in the $$y$$-coordinates.
  2. Describe that the distance formula is derived from the Pythagorean Theorem, where a is represented by the change in the $$x$$-coordinates of the leg of a triangle and b is represented by the change in the $$y$$-coordiantes of the leg of a triangle. 
  3. Derive the distance formula of $$d=\sqrt{(x_{2}-x_1)^2+(y_2-y_1)^2}$$.
  4. Calculate the area and perimeter of basic polygons where the side lengths are diagonal line segments on a coordinate plane. 

Tips for Teachers


Anchor Problem #2 will require the teacher to do a significant amount of modeling to derive the distance formula from the Pythagorean Theorem.

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Anchor Problems


Problem 1

What is the length of each of the line segments shown below?

Guiding Questions

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Problem 2

Amy knows that the distance between two points is derived from the Pythagorean Theorem. Show how Amy gets from the Pythagorean Theorem to the “distance formula.”

Guiding Questions

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Target Task


Find the perimeter and area (in units) of the following rectangle.

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 must find the area and perimeter of a polygon on the coodinate plane.
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Lesson 2

Lesson Map

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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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