![\left[\begin{array}{ccc}a&b&1\\c&d&1\\e&f&1\end{array}\right]](/tpl/images/1408/0545/41361.png)
and calculate the determinant of that. Three points on the parallelogram are (-1,1), (-1, -5), and (4, 5). Plugging these into the matrix, we get![\left[\begin{array}{ccc}-1&1&1\\-1&-5&1\\4&5&1\end{array}\right]](/tpl/images/1408/0545/7f89c.png)
. The determinant is equal to![-1 *det \left[\begin{array}{ccc}-5&1\\5&1\end{array}\right] \\- 1 * det \left[\begin{array}{ccc}-1&1\\4&1\end{array}\right] \\\\+ 1 * det \left[\begin{array}{ccc}-1&-5\\4&5\end{array}\right] \\= -1 * (-5*1 - (1*5))- 1 * (-1 * 1 - (4*1)) + 1 * (-1 * 5 - (-5*4)) \\= -1 *(-5-5) -1 * (-1 - 4) + 1 * (-5 - (-20))\\= -1 * (-10) -1 * (-5) +1 * (15)\\= 10 + 5 + 15\\=30](/tpl/images/1408/0545/4906c.png)
Use determinants to find the area of the parallelogram shown below
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Mathematics, 12.08.2021 21:30 Kizmit4938
Use determinants to find the area of the parallelogram shown below
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