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Q&A #730


Perpendicular Lines & Gradients

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From: Marielouise (for Teacher2Teacher Service)
Date: Nov 01, 1998 at 16:29:39
Subject: Re: Perpendicular Lines & Gradients

Teo,

I think that you are doing an excellent job by doing all that you have done 
above.  I especially like that two trig approaches.  I honestly do not know 
of any games but I can relate to you an activity that I have used with 
freshmen trying to discover the relationship between slopes of perpendicular 
lines.

1.  The students have to agree that the sides of a rectangle are
perpendicular because the angles formed are right angles.

2.  Prepare several rectangles cut from tagboard paper or file folders.  
Determine ahead of time what the dimensions will be. Try to be very accurate
in your cutting. Select a piece of graph paper that the students shall use.
From the graph paper decide the length of the width and length of the
rectangle so that the slope of the line is a number like 2/3.

3.  In essence what you are trying to do is devise rectangles so that the 
points lie on lattice points of the graph paper. You do not wish to choose 
lattice points so that the slope is zero or undefined. For example, (0,0), 
(6, 1), (-1,6) and (5,7) give you slopes of -6 and 1/6.

4.  The goal of the activity is for the students to fit the rectangles on the 
graph paper, record the lattice points, find the slope of the lines between 
adjacent points and to show that the slopes of the adjacent lines are 
negative reciprocals of each other.

5.  The key to this activity is for you to determine the proper rectangles 
that will give you integer lattice points.

This is not a game, but an activity that can be done with a partner and that
leads to discovery.

 -Marielouise, for the Teacher2Teacher service

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