# Pythagorean Theorem Investigation with Distance and Midpoint Formulas

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(705 KB|6 pages)
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Students will love puzzling out hiking destinations with this Pythagorean theorem investigation!

This lesson includes a simple, visual proof of the Pythagorean Theorem followed by an activity where students use locations to determine distance and midpoint between two points. A summary at the end of class will bring home the main ideas:

The coordinates of two points can be used to find the distance directly between them (both graphically and with the distance formula).

The coordinates of two points can be used to find their midpoint (both graphically and with the midpoint formula).

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Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohmβs law π = π­π to highlight resistance π.
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Total Pages
6 pages
N/A
Teaching Duration
1 hour
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