In Exercises 19–22, find the area of the parallelogram whose vertices are listed.

(0,-2),(5,-2),(-3,1),(2,1)

find the

hansel

Answered by Aaron 2 years ago

Translate the coordinates so that one of them is at the origin, doing so *does not change the area* of the parallelogram, but allows us to find the area.

In this case I will add the vector (0,2) to each vertex which gives,

(0,0),(5,0),(-3,3),(2,3)

let

Now the area of the parallelogram is the determinant of the matrix formed by the column vectors (5,0) and (-3,3),

$$ \begin{vmatrix} 5 & -3 \\ 0 & 3 \end{vmatrix}=15 $$

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Asked: 2 years ago