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The Shortest Distance

Overview | Activities

Overview:

This lesson will help students make connections between two math disciplines for problem solving: algebra and geometry. The Pythagorean theorem is probably one of the most widely recognized and remembered formulas from high school math class. Building on the momentum of memory, students will derive the less-familiar distance formula from the very familiar a² + b² = c² expression.

Subject Matter: Math

Learning Objectives:

Learners will be able to:
• identify appropriate steps used to resolve unknown sides of a right triangle
• express the square root function as an exponential function
• algebraically derive the distance formula using principles of geometry
Standards:

http://www.emsc.nysed.gov/guides/mst/perf.pdf
Standard 3: Math, Science and Technology - Intermediate Level
Students will develop and apply the Pythagorean principle in the solution of problems.

Media components:

Animated Proof of the Pythagorean Theorem
http://www.usna.edu/MathDept/mdm/pyth.html
This animation will allow students to understand better what is meant by "sum of the squares for each side." Right triangle geometry is given a broader context with this short animation.

Demonstrate the Pythagorean Theorem
http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html
This companion web site for the PBS program NOVA is a manual tool useful for replicating the animation. The site offers real-world connections by using baseballs and ladders as a context for problem solving. (Requires Flash Player)

Distance Formula
http://www.astro.washington.edu/labs/clearinghouse/labs/distform.html
This interactive site provides an overview of the distance formula showing its derivation using right triangle representation.

Distance Formula
http://www.purplemath.com/modules/distform.htm
This site provides a well-organized explanation of the distance formula derivation. It shows how to find the distance of a line created by two points of a triangle.

Supplies:
• Metric ruler
• Graph paper (See Handouts, Graphing the Solution)
• Calculator
• Scrap paper

Handouts