Involution: Point pairs on a line

On a given line, if two ranges I and II are defined, then we can assign a point on the line to either range. Consider a projection I → II, where at the same time A → A' A' → A Then {A, A'} are referred to as a [i]conjugate pair.[/i] If, in a projection two pairs of corresponding points are conjugate, then every pair is conjugate (Desargues). The projection is determined, but what is it? Given conjugate pairs {A, A'}, {B, B'}, and an arbitrary point C on the same line, where is C'? ___________ Double Point -- Let C and C' coincide: [url]http://www.geogebratube.org/material/show/id/243957[/url]

 

Ryan Hirst

 
Resource Type
Activity
Tags
desargues  involution  pairs  point 
Target Group (Age)
14 – 18
Language
English (United States)
 
 
GeoGebra version
4.4
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4117
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