document.write( "Question 1207834: Rewrite the statement using absolute value notation. \r
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\n" ); document.write( "\n" ); document.write( "The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin. \n" ); document.write( "

Algebra.Com's Answer #845961 by ikleyn(52834) $\"\"$ $\"About$

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\n" ); document.write( "Rewrite the statement using absolute value notation.\r
\n" ); document.write( "\n" ); document.write( "The sum of the distances of a and b from the origin is greater
\n" ); document.write( "than or equal to the distance of a + b from the origin.
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\n" ); document.write( "\n" ); document.write( " I don't know, at what scene the action of this play takes place: in the number line,\r
\n" ); document.write( "\n" ); document.write( " or in a plane (2D), or in space (3D). But I will tell the story, assuming that the play is on a plane (2D).\r
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document.write( "    |a| + |b| >= |a+b|.    ANSWER\r\n" );
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document.write( "Explanation\r\n" );
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document.write( "On the plane, we have the origin O;\r\n" );
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document.write( "    point A at the distance \"a\" from O (represents vector OA of the length \"a\");\r\n" );
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document.write( "    point B at the distance \"b\" from O (represents vector OB of the length \"b\").\r\n" );
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document.write( "In this interpretation, a+b is the third side of the triangle OAB (the parallelogram rule of adding vectors).\r\n" );
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document.write( "Then the triangle inequality says that \r\n" );
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document.write( "    |a| + |b| >= |a+b|.\r\n" );
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document.write( "It is precisely what they want you prove.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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