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A dilation is an isometry.

 Feb 5, 2017
 #1
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False

 Feb 5, 2017
 #2
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A dilation is an isometry if (r,t) --> (kr,t), where k > 1.

 

T: x --> u

x = (x,y) = (rcost, rsint)

u = (u,v) = (krcost, krsint) = k(rcost, rsint) = kx

 

T is an isometry if u/kr = x/r, which is in fact the case here in this question.

 Feb 5, 2017

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