document.write( "Question 1027077: Point P is inside rectangle ABCD. Show that
\n" ); document.write( "PA^2 + PC^2 = PB^2 + PD^2.\r
\n" ); document.write( "\n" ); document.write( "Be sure that your proof works for ANY point inside the rectangle. \n" ); document.write( "

Algebra.Com's Answer #642359 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Point P is inside rectangle ABCD. Show that
\n" ); document.write( "PA^2 + PC^2 = PB^2 + PD^2.\r
\n" ); document.write( "\n" ); document.write( "Be sure that your proof works for ANY point inside the rectangle.
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document.write( "Let us assume that \r\n" );
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document.write( "  - the vertice A of the rectangle has the coordinates (0,0)   (lies at the origin)\r\n" );
document.write( "  - the vertice B                                      (a,0),\r\n" );
document.write( "  - the vertice C                                      (a,b),   and\r\n" );
document.write( "  - the vertice D                                      (0,b).\r\n" );
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document.write( "Let the point P is (x,y).\r\n" );
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document.write( "Then \r\n" );
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document.write( " = .\r\n" );
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document.write( " = ,\r\n" );
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document.write( "according to the Pythagorean theorem.\r\n" );
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document.write( "Compare these formulas to make sure that the right sides are equal.\r\n" );
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document.write( "So the left sides are.\r\n" );
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document.write( "Proved.\r\n" );
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