document.write( "Question 1197664: Hi, can you help me solve this problem?
\n" ); document.write( "Given a quadrilateral whose vertices are ( 3, 5 ) , ( 4, -1 ), ( 8, -2 ) and ( 9, 7 ), show
\n" ); document.write( "that the line segments joining the midpoints of adjacent sides from a parallelogram. \n" ); document.write( "
Algebra.Com's Answer #831031 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll do all but the last two steps.\r\n" );
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document.write( "We use the midpoint formula to find the midpoints of the sides:\r\n" );
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document.write( "Midpoint =  \r\n" );
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document.write( "Midpoint of the top side:\r\n" );
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document.write( "Midpoint = \"%28matrix%281%2C3%2C%283%2B9%29%2F2%2C+%22%2C%22%2C%285%2B7%29%2F2%29%29\" =\r\n" );
document.write( "           \"%28matrix%281%2C3%2C12%2F2%2C+%22%2C%22%2C12%2F2%29%29\"\r\n" );
document.write( "           \"%28matrix%281%2C3%2C6%2C+%22%2C%22%2C6%29%29\"\r\n" );
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document.write( "Midpoint of the left side:\r\n" );
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document.write( "Midpoint = \"%28matrix%281%2C3%2C%283%2B4%29%2F2%2C+%22%2C%22%2C%285%2B%28-1%29%29%2F2%29%29\" =\r\n" );
document.write( "           \"%28matrix%281%2C3%2C7%2F2%2C+%22%2C%22%2C4%2F2%29%29\"\r\n" );
document.write( "           \"%28matrix%281%2C3%2C3.5%2C+%22%2C%22%2C2%29%29\"\r\n" );
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document.write( "Midpoint of the bottom side:\r\n" );
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document.write( "Midpoint = \"%28matrix%281%2C3%2C%284%2B8%29%2F2%2C+%22%2C%22%2C%28-1%2B%28-2%29%29%2F2%29%29\" =\r\n" );
document.write( "           \"%28matrix%281%2C3%2C12%2F2%2C+%22%2C%22%2C-3%2F2%29%29\"\r\n" );
document.write( "           \"%28matrix%281%2C3%2C6%2C+%22%2C%22%2C-1.5%29%29\"\r\n" );
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document.write( "Midpoint of the right side:\r\n" );
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document.write( "Midpoint = \"%28matrix%281%2C3%2C%288%2B9%29%2F2%2C+%22%2C%22%2C%28-2%2B7%29%2F2%29%29\" =\r\n" );
document.write( "           \"%28matrix%281%2C3%2C17%2F2%2C+%22%2C%22%2C5%2F2%29%29\"\r\n" );
document.write( "           \"%28matrix%281%2C3%2C8.5%2C+%22%2C%22%2C2.5%29%29\"\r\n" );
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document.write( "Now we just need to show that the two pairs of opposite sides are parallel\r\n" );
document.write( "by showing that the pairs have the same slope.\r\n" );
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document.write( "We use the slope formula:\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "where (x1,y1) = (6,6)\r\n" );
document.write( "and where (x2,y2) = (3.5,2)\r\n" );
document.write( "\"m\"\"%22%22=%22%22\"\"%286-2%29%2F%286-3.5%29\"\r\n" );
document.write( "\"m\"\"%22%22=%22%22\"\"4%2F%282.5%29\"\"%22%22=%22%22\"\"1.6%29\"\r\n" );
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document.write( "We find the slope of its opposite side\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "where (x1,y1) = (6,-1.5)\r\n" );
document.write( "and where (x2,y2) = (8.5,2.5)\r\n" );
document.write( "\"m\"\"%22%22=%22%22\"\"%282.5-%28-1.5%29%29%2F%288.5-6%29\"\r\n" );
document.write( "\"m\"\"%22%22=%22%22\"\"%282.5%2B1.5%29%2F2.5\"\r\n" );
document.write( "\"m\"\"%22%22=%22%22\"\"%284%29%2F%282.5%29\"\"%22%22=%22%22\"\"1.6%29\"\r\n" );
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document.write( "So that shows that those two green sides are parallel,\r\n" );
document.write( "since their slopes are both 1.6.\r\n" );
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document.write( "I'm going to stop here and let you finish on your own by\r\n" );
document.write( "showing that the slopes of the other pair of opposite sides \r\n" );
document.write( "are also parallel, by showing that they have the same slope \r\n" );
document.write( "also, by the same method.\r\n" );
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document.write( "The problem will not be complete until you do this last part.\r\n" );
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document.write( "Edwin
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