document.write( "Question 906961: I have a problem that asks me to:\r
\n" ); document.write( "\n" ); document.write( "*Find the area of each parallelogram.
\n" ); document.write( "*Write an equation for side of each parallelogram.
\n" ); document.write( "*What do you notice about the slope of the opposite sides of each parallelogram?\r
\n" ); document.write( "\n" ); document.write( "Then it shows me a graph with a parallelogram on it. I don't have an example in my math book to help me figure out how to work it out and I don't understand it. \n" ); document.write( "
Algebra.Com's Answer #550119 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll make up a problem like that.\r\n" );
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document.write( "Parallelogram ABCD has vertices A(-4,2), B(-5,-3), C(3,-1), D(4,4).\r\n" );
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document.write( "Find the slope and equation of of AB:\r\n" );
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document.write( "Slope formula:\r\n" );
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document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
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document.write( "where (x1,y1) = A(-4,2)\r\n" );
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document.write( "and where (x2,y2) = B(-5,-3)\r\n" );
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document.write( "m = \"%28%28-3%29-%282%29%29%2F%28%28-5%29-%28-4%29%29\"\r\n" );
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document.write( "m = \"%28-3-2%29%2F%28%28-5%2B4%29%29\"\r\n" );
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document.write( "m = \"%28-5%29%2F%28-1%29\"\r\n" );
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document.write( "m = \"5\"\r\n" );
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document.write( "Point-slope formula:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
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document.write( "where (x1,y1) = (-4,2)\r\n" );
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document.write( "y - (2) = (5)(x - (-4))\r\n" );
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document.write( "  y - 2 = 5(x + 4)\r\n" );
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document.write( "  y - 2 = 5x + 20\r\n" );
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document.write( "      y = 5x + 22  <-- equation of AB, slope = 5\r\n" );
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document.write( "Using the same method find the equations of the other three sides:\r\n" );
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document.write( "      \"y=expr%281%2F4%29x-7%2F4%29\" <-- equation of BC, slope = \"1%2F4\" \r\n" );
document.write( "      \"y=5x-16\"  <-- equation of CD, slope = 5 \r\n" );
document.write( "      \"y=expr%281%2F4%29x%2B3%29\" <-- equation of AD, slope = \"1%2F4\"\r\n" );
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document.write( "Notice that opposite sides AB and CD both have slope = 5\r\n" );
document.write( "Notice that opposite sides BC and AD both have slope = \"1%2F4\"\r\n" );
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document.write( "That demostrates that opposite sides of a parallelogram are parallel,\r\n" );
document.write( "i.e., they have the same slope.\r\n" );
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document.write( "To find the area, find the area of the triangle ABC by the determinant\r\n" );
document.write( "method and double it.\r\n" );
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document.write( "The determinant formula for the area of a triangle is\r\n" );
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document.write( "A = \r\n" );
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document.write( "Where the x's and y's are the three coordinates of the vertices \r\n" );
document.write( "in order taken counterclockwise around the triangle.\r\n" );
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document.write( "A = \r\n" );
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document.write( "Area of the parallelogram = 2×19 = 38\r\n" );
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document.write( "Edwin
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