document.write( "Question 879410: Show that the triangle with vertices (-4,-3), (√27, -√48) and (4,3) is equilateral. \n" ); document.write( "
Algebra.Com's Answer #530856 by Edwin McCravy(20066)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "We use the distance formula on all three sides to show\r\n" );
document.write( "that all the sides have the same length.\r\n" );
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document.write( "Distance from (-4,-3), (√27, -√48)\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%28x%5B2%5D-x%5B1%5D%29%5E2+%2B+%28y%5B2%5D-y%5B1%5D%29%5E2%29\" \r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%28%28sqrt%2827%29%29-%28-4%29%29%5E2+%2B+%28%28-sqrt%2848%29%29-%28-3%29%29%5E2%29\" \r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%28sqrt%2827%29%2B4%29%29%5E2+%2B+%28-sqrt%2848%29%2B3%29%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%2827%2B8sqrt%2827%29%2B16+%2B+48-6sqrt%2848%29%2B9%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100+%2B+8sqrt%289%2A3%29-6sqrt%2816%2A3%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100+%2B+8%2A3sqrt%283%29-6%2A4sqrt%283%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100+%2B+24sqrt%283%29-24sqrt%283%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"10\"\r\n" );
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document.write( "-------------------------------\r\n" );
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document.write( "Distance from (-4,-3) to (4,3)\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%28x%5B2%5D-x%5B1%5D%29%5E2+%2B+%28y%5B2%5D-y%5B1%5D%29%5E2%29\" \r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%28%284%29-%28-4%29%29%5E2+%2B+%28%283%29-%28-3%29%29%5E2%29\" \r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%284%2B4%29%5E2+%2B+%283%2B3%29%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%288%29%5E2+%2B+%286%29%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%2864+%2B+36%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"10\"\r\n" );
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document.write( "--------------------------------------\r\n" );
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document.write( "Distance from (4,3) to (√27, -√48)\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%28x%5B2%5D-x%5B1%5D%29%5E2+%2B+%28y%5B2%5D-y%5B1%5D%29%5E2%29\" \r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%28%28sqrt%2827%29%29-%284%29%29%5E2+%2B+%28%28-sqrt%2848%29%29-%283%29%29%5E2%29\" \r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28+%28sqrt%2827%29-4%29%29%5E2+%2B+%28sqrt%2848%29-3%29%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%2827-8sqrt%2827%29%2B16+%2B+48%2B6sqrt%2848%29%2B9%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100+-+8sqrt%289%2A3%29%2B6sqrt%2816%2A3%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100+-+8%2A3sqrt%283%29%2B6%2A4sqrt%283%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100+-+24sqrt%283%29%2B24sqrt%283%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"d\"\"%22%22=%22%22\"\"+sqrt%28100%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"10\"\r\n" );
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document.write( "All three sides are equal to 10, so the triangle is equilateral.\r\n" );
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document.write( "Edwin
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