find the area of the parallelogram whose vertices are listed

# find the area of the parallelogram whose vertices are listed

H
240 points

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

8.7k points

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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