document.write( "Question 1078312: Please help me solve this. Use determinants to find the area of the parallelogram shown at the link below. \r
\n" ); document.write( "\n" ); document.write( "Parallelogram: https://s27.postimg.org/g9xivnbbn/figurefor16.png \n" ); document.write( "
Algebra.Com's Answer #692823 by ikleyn(52787)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "    If  u = \"%28matrix%282%2C1%2C+a%2C+c%29%29\"  and  v = \"%28matrix%282%2C1%2C+b%2C+d%29%29\"  are vectors in a coordinate plane, then the area of the parallelogram which is built on these vectors \r\n" );
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document.write( "    as on sides is equal to the modulus of the determinant,  |det \"%28matrix%282%2C2%2C+a%2C+b%2C+c%2C+d%29%29\"|,  of the  2x2-matrix  A = \"%28matrix%282%2C2%2C+a%2C+b%2C+c%2C+d%29%29\"  whose columns are the given vectors.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For the proof of this theorem see the lesson \r
\n" ); document.write( "\n" ); document.write( "    - Determinant of a 2x2-matrix and the area of a parallelogram and a triangle \r
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document.write( "Your vector U is the vertical side of the parallelogram from the point (-1,-5) to the point (-1,1).\r\n" );
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document.write( "It has component form U = (-1-(-1),1-(-5)) = (-1+1, 1+6) = (0,7).\r\n" );
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document.write( "Your vector V is the sloped side of the parallelogram from the point (-1,-5) to the point (4,5).\r\n" );
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document.write( "It has component form V = (4-(-1),5-(-5)) = (4+1, 5+5) = (5,10).\r\n" );
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document.write( "Now make a matrix A whose columns are the components of the vectors U and V:\r\n" );
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document.write( "    A = \"%28matrix%282%2C2%2C+0%2C5%2C+7%2C10%29%29\".\r\n" );
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document.write( "Then take its determinant  det(A) = det \"%28matrix%282%2C2%2C+0%2C5%2C+7%2C10%29%29\" = -5*7 = -35.\r\n" );
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document.write( "Finally, take the modulus of the determinant, i.e. its absolute value.\r\n" );
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document.write( "You will get the area of your parallelogram\r\n" );
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document.write( "    S = | det (A) | = |-35| = 35.\r\n" );
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document.write( "Answer.  The area of the parallelogram is 35 square units.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There are lessons in this site relevant to this theme:\r
\n" ); document.write( "\n" ); document.write( "    - What is a matrix?,\r
\n" ); document.write( "\n" ); document.write( "    - Determinant of a 2x2-matrix,\r
\n" ); document.write( "\n" ); document.write( "    - Determinant of a 2x2-matrix and the area of a parallelogram and a triangle. \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "     \"2x2-Matrices, determinants, Cramer's rule for systems in two unknowns\" \r
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