Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

Linear Transformation problem

Find all real values of a and b such that the following is a reflection

T:  X  =  aX + (24/25)Y
     Y      bY + (24/25)X     

Sorry for the lack of latex; I'm sure you can work it out.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Linear Transformation problem

So this answers the question I asked about your previous problem.  You are looking for a matrix solution.

If you transform (0,0) you get (0,0), so this transformation has the origin as an invariant point.

If it is to be a reflection, the line must have the form y = mx;  and a point and its reflected image must lie on the line y = -x/m +c

That should be enough to identify the reflection.

You might find this page helpful:

http://planetmath.org/derivationof2dreflectionmatrix

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob