Area of parallelogram (matrix)

  1. How co you claculate the are a pallelogram determined by points (-2, -2), (0, 3), (4, -1) and (6, 4)...I've seen an example wher a 2x2 determinant matrix was used, but I don't remember how to do it...
     
  2. jcsd
  3. Galileo

    Galileo 1,999
    Science Advisor
    Homework Helper

    The absolute value of the determinant of a 2x2 matrix is the area of the parallelogram determined by the column (or row) vectors of the matrix.
     
  4. I was explained that I should take the opposite points, in a form of
    |x1 x2|
    |y1 y2| and if the parallelogram is above the x axis, then the area is positive else its negative...so the determinants I have tried,

    |-2 6|
    |-2 4| and det = 4 but if I use the other two points I get a different answer

    |0 4|
    |3 -1| and det = 12 but once I draw the parallelogram I found the area to be 6x5=30...what am I doing wrong?
     
  5. Galileo

    Galileo 1,999
    Science Advisor
    Homework Helper

    You've drawn the parallelogram. So can you see the vectors which determine that parallelogram?
     
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