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Q&A #6276


Use of matrices in transformation

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From: Joshua (for Teacher2Teacher Service)
Date: May 07, 2001 at 19:15:00
Subject: Re: Use of matrices in transformation

Hi Ghania,
to continue from where Pat left off, some matrices like
[1 3] [x]
[2 6] [y]

will give an image of
[ x+3y]
[2x+6y]

which is, as he pointed out, the line y' = 2x'.

I'd just like to ask and answer the question: what shapes have images that are 
just a single point under this transformation?

The answer is any set of points where x + 3y is a constant for all points in 
the set:  that is, points along any line
x + 3y = c, or y = -1/3 x + C.

That is, all lines or segments with slope -1/3 are mapped to a single point.

 -Joshua, for the T2T service

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