How do you calculate the area of a parallelogram using a determinant matrix?

[niteshadw]

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...

 

[Galileo]

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.

 

[niteshadw]

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?

 

[Galileo]

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