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Finding transformation T such that T(D*)=D

  1. Nov 14, 2016 #1
    1. The problem statement, all variables and given/known data
    If ##D^*## is the parallelogram whose vertices are ##(0,0)##,##(-1,3)##, ##(1,2)##, and ##(0,5)## and D is the parallelogram whose vertices are ##(0,0)##, ##(3,2)##,##(1,-1)## and ##(4,1)##, find a transformation ##T## such that ##T(D^*)=D##.

    2. Relevant equations


    3. The attempt at a solution
    From drawing both parallelograms, the point ##(0,0)## maps to ##(0,0)##, point ##(-1,3)## maps to ##(3,2)##, point ##(0,5)## maps to ##(4,1)## and point ##(1,2)## maps to ##(1,-1)##.

    I really have no idea how to figure out the transformation. I don't see any pattern at all. Any hints?

    Thanks!
     
  2. jcsd
  3. Nov 14, 2016 #2

    Ray Vickson

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    Represent ##T## by a ##2 \times 2## matrix, and figure out what must be the four entries of the matrix.
     
  4. Nov 15, 2016 #3
    Ah, thanks. I've got it!
     
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