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

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Homework Help Overview

The discussion revolves around calculating the area of a parallelogram using a determinant matrix, specifically with points given in a coordinate system. The subject area includes geometry and linear algebra concepts related to determinants and vector representation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the determinant method using coordinates of the parallelogram's vertices but expresses confusion over the calculations and results. Some participants discuss the relationship between the determinant and the area, while others question the choice of points and the interpretation of the determinant's sign.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the determinant method. There is an indication that some guidance has been offered regarding the vectors that define the parallelogram, but no consensus has been reached on the correct approach or calculations.

Contextual Notes

The original poster mentions discrepancies in area calculations based on different pairs of points, suggesting potential misunderstandings about the setup or the determinant's application. There may also be confusion regarding the geometric interpretation of the determinant's sign.

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

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