# Isometries of R2

• Jan 3rd 2012, 04:06 PM
Bernhard
Isometries of R2
I am reading Aigli Papantonopoulou's book Algebra: Pure and applied.

Exercise 16 of Chapter 14:Symmetries reads as follows:

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"Find all isometries of $\mathbb{R}^2$ that map the line y = x to the line y = 1 - 2x

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Peter
• Jan 4th 2012, 04:30 AM
Deveno
Re: Isometries of R2
rather than give you the actual answer, i will give you the basic idea: how do you place one long skinny stick, on top of another? well, you can just put it directly on top, or you can "twirl it around", and then set it down, or you can "flip it over". does this give you any idea of how to proceed?
• Jan 4th 2012, 06:22 PM
Bernhard
Re: Isometries of R2