Find the area of the parallelogram whose vertices are listed. (0,0), (5,2), (6,4

Cabiolab 2021-09-27 Answered
Find the area of the parallelogram whose vertices are listed. (0,0), (5,2), (6,4), (11,6)

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Expert Answer

Aniqa O'Neill
Answered 2021-09-28 Author has 12976 answers

Parallelogram can be described with 4 vertices or 2 vectors. Since we are given 4 vertices(ABCD), let's find vectors u, v that describe parallelogram. Graph these points to see how vectors are described
A=(0,0)
B=(5,2)
C=(6,4)
D=(11,6)
\(u=AB=\begin{bmatrix}5\\2\end{bmatrix}\)
\(u=AC=\begin{bmatrix}6\\4\end{bmatrix}\)
Area of parallelogram is absolute value of determinant
\(\begin{bmatrix}u_1 & v_1 \\u_2 &v_2 \end{bmatrix}\)
\(\begin{bmatrix}u_1 & v_1 \\u_2 &v_2 \end{bmatrix}=det\begin{bmatrix}5& 6 \\2 &4 \end{bmatrix}=20-12=8\)
Result:
8

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