Composition of Two Dilations

What happens when you compose two dilations (enlargements)? When they share a centre it's easy, but when the centres are in different places then it's not even obvious that the composition is actually a dilation. This sketch allows you to explore this situation by seeing what happens to a quadrilateral when it is transformed by two dilations. It was inspired by [url=https://twitter.com/jamestanton/status/567307177589620737]a tweet by James Tanton[/url]. Spoiler: In general the composition [b]is[/b] a dilation, with the centre of the overall transformation lying between the centres of the two original dilations in the ratio (b-1):b(a-1), where a and b are the scale factors. There are special cases, and in particular when ab=1 the composite transformation is a translation rather than a dilation.

 

Jon Ingram

 
Resource Type
Activity
Tags
dilation  enlargement  geometry  transformations 
Target Group (Age)
14 – 18
Language
English
 
 
GeoGebra version
5.0
Views
4668
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