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.
