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Finding area of the affine translation of a rectangle

  1. Mar 18, 2015 #1
    1. The problem statement, all variables and given/known data
    Given a rectangle R=[1,3] x [2,4], and the affin translation F : R^2 -> R^2 defined by F(x,y) = (1,3) + A*(x,y), where A is the 2x2 matrix (2 , 7 ; 3 , 1), what is the area of the affin transelation of the rectangle R?

    2. Relevant equations


    3. The attempt at a solution
    When I cross the vectors of R I get the scalar 2. Is this the area of R before we transelate it? The determinant of A equals 19, and 2*19=38. So this is my answer and it is wrong. Right answer is 76, so I guess the area of R before translation should be 76/det(A)=4. Where am I wrong?
     
  2. jcsd
  3. Mar 18, 2015 #2

    LCKurtz

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    The area of R is obiously 2x2=4 and it must be multiplied by 19 to get the translated area. What are the "vectors of R" that you crossed? Show us that.
     
  4. Mar 18, 2015 #3
    R = [1,3] cross [2,4], so I think the vectors of R are [1,3] and [2,4] . When they are crossed the product is abs(4-6) = 2. I want the answer to be 4, but I don't know how!
     
  5. Mar 18, 2015 #4

    LCKurtz

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    Those are not the correct vectors to cross. You want the vectors along the sides of the square.
     
  6. Mar 18, 2015 #5

    Mark44

    Staff: Mentor

    In addition to what LCKurtz said, those aren't even vectors -- they are intervals along the x and y axes. Also, I don't know what you are doing when you say you are "crossing" these vectors. The vector cross product is defined for vectors in R3.
     
  7. Mar 19, 2015 #6
    Okey, I misunderstood R = [1,3] x [2,4]. Then i makes sense that the area of R is 4 and 4*19=76 after the translation. Thanks!
     
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