document.write( "Question 814754: Classify Triangle DEF with vertices D(2,3), E(5,7), and F(9,4)
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Algebra.Com's Answer #490489 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let's plot it and see:\r\n" );
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document.write( "It's pretty clear that angles D and F are acute.  Hoever angle E\r\n" );
document.write( "looks suspiciously like it just might be a right angle.  To find out\r\n" );
document.write( "we need to find the slopes of DE and EF to find out if they are \r\n" );
document.write( "perpendicular.  To find that out we find whether the slope of \r\n" );
document.write( "one is the reciprocal of the other with the sign changed.\r\n" );
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document.write( "Find the slope of DE\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) = (2,3)\r\n" );
document.write( "and where (x2,y2) = (5,7)\r\n" );
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document.write( "m = \"%287-3%29%2F%285-2%29\" = \"4%2F3\".\r\n" );
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document.write( "Find the slope of EF\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) = (5,7)\r\n" );
document.write( "and where (x2,y2) = (9,4)\r\n" );
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document.write( "m = \"%284-7%29%2F%289-5%29\" = \"%28-3%29%2F4\" = \"-3%2F4\"\r\n" );
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document.write( "So oe slope is \"4%2F3\" and the other is \"-3%2F4\",\r\n" );
document.write( "which is the recipocal of \"4%2F3\" with the sign \r\n" );
document.write( "changed.\r\n" );
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document.write( "So the  sides DE and EF are perpendicular and therefore\r\n" );
document.write( "the triangle is a right triangle.\r\n" );
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document.write( "It also looks like it might be isosceles, with DE and EF\r\n" );
document.write( "equal. so let's find the lengths of the legs DE and EF \r\n" );
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document.write( "d = √(x2-x1)²+(y2-y1)²\r\n" );
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document.write( "For DE\r\n" );
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document.write( "d = √(5-2)²+(7-3)²  \r\n" );
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document.write( "d = √(3)²+(4)²\r\n" );
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document.write( "d = √9+16\r\n" );
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document.write( "d = √25\r\n" );
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document.write( "d = 5\r\n" );
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document.write( "For EF\r\n" );
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document.write( "d = √(9-5)²+(4-7)²  \r\n" );
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document.write( "d = √(4)²+(-3)²\r\n" );
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document.write( "d = √16+9\r\n" );
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document.write( "d = √25\r\n" );
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document.write( "d = 5\r\n" );
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document.write( "So triangle DEF is also an isosceles triangle as well as a right triangle.\r\n" );
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document.write( "Edwin
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