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Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Standard #: MAFS.8.G.2.8Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Geometry
Cluster: Level 1: Recall
Cluster: Understand and apply the Pythagorean Theorem. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
Formative Assessments
Lesson Plans
  • As the Crow Flies # This two-day lesson teaches students to use the Pythagorean Theorem with simple right triangles on the first day, then progresses to using the theorem to find the distance between two points on a coordinate graph.
  • Discover and Make Sense of the Pythagorean Theorem # This lesson unit helps teachers assess how well students can use the area of right triangles to deduce the areas of other shapes, use dissection methods for finding areas, organize an investigation systematically, and collect data to deduce a generalizable method for finding lengths and areas (The Pythagorean Theorem).
  • Bike Club Trip # In this activity the students will rank different locations for a bike club's next destination. In order to do so, the students must use Pythagorean Theorem and well as analyze data of the quantitative and qualitative type. Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
  • Alas, Poor Pythagoras, I Knew You Well! #2 # Using different activities, students will find real life uses for the Pythagorean Theorem.
Perspectives Video: Professional/Enthusiasts
Presentation/Slideshow
  • Pythagoras' Theorem # This resource can be used to introduce the Pythagorean Theorem to students. It provides sketches, applets, examples and easy-to-understand visual proofs as well as an algebra proof for the theorem.

    It also includes interactive multiple choice practice questions on solving for a side of a right triangle, and applications involving right triangles, as well as a hands-on activity for students to do that allows them to create their own proof.
Problem-Solving Tasks
  • A Rectangle in the Coordinate Plane # This task provides an opportunity to apply the Pythagorean theorem to multiple triangles in order to determine the length of the hypotenuse; the converse of the Pythagorean theorem is also required in order to conclude that certain angles are right angles.
  • Bird and Dog Race # The purpose of this task is for students to use the Pythagorean Theorem as a problem-solving tool to calculate the distance between two points on a grid. In this case the grid is also a map, and the street names can be viewed as defining a coordinate system (although the coordinate system is not needed to solve the problem).
  • Is This a Rectangle? # The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. Creativity will be essential here as the only given information is the Cartesian coordinates of the quadrilateral's vertices. Using this information to show that the four angles are right angles will require some auxiliary constructions. Students will need ample time and, for some of the methods provided below, guidance. The reward of going through this task thoroughly should justify the effort because it provides students an opportunity to see multiple geometric and algebraic constructions unified to achieve a common purpose. The teacher may wish to have students first brainstorm for methods of showing that a quadrilateral is rectangle (before presenting them with the explicit coordinates of the rectangle for this problem): ideally, they can then divide into groups and get to work straightaway once presented with the coordinates of the quadrilateral for this problem.
Text Resources
  • Pythagoras Explained # This informational text resource is intended to support reading in the content area. The text describes a method for predicting the win-loss record for baseball teams based on runs scored and runs allowed, using the "Pythagorean Expectation" formula invented by Bill James. The text goes on to show the relationship of the prediction formula to the Pythagorean theorem, pointing out a very cool application of the theorem to the world of sports.
  • The Pythagorean Theorem # This overview of the Pythagorean Theorem covers its purpose, equation, application, and validity. The site also provides a number of illustrations which help students visualize the theorem, and links to related resources for further understanding.
Tutorial
  • Distance formula and the Pythagorean Theorem # This tutorial shows students how to find the distance between lines using the Pythagorean Theorem. This video makes a connection between the distance formula and the Pythagorean Theorem.
STEM Lessons - Model Eliciting Activity
  • Bike Club Trip # In this activity the students will rank different locations for a bike club's next destination. In order to do so, the students must use Pythagorean Theorem and well as analyze data of the quantitative and qualitative type. Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
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