document.write( "Question 429188: Use coordinates to prove that the diagonals of a rectangle are equal in length. \n" ); document.write( "

Algebra.Com's Answer #298248 by richard1234(7193) $\"\"$ $\"About$

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Since the position of the rectangle is irrelevant, we can assume (without loss of generality, a common math expression) that the vertices of the rectangle are at points (0,0), (a,0), (a,b), and (0,b). The diagonals are determined by the sets of points {(0,0), (a,b)} and {(a,0), (0,b)}. We use the distance formula to find each distance:\r
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\n" ); document.write( "\n" ); document.write( "{(0,0), (a,b)}\r
\n" ); document.write( "\n" ); document.write( " $\"d%5B1%5D+=+sqrt%28%28a-0%29%5E2+%2B+%28b-0%29%5E2%29+=+sqrt%28a%5E2+%2B+b%5E2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "{(a,0),(0,b)}\r
\n" ); document.write( "\n" ); document.write( " $\"d%5B2%5D+=+sqrt%28%280-a%29%5E2+%2B+%28b-0%29%5E2%29+=+sqrt%28a%5E2+%2B+b%5E2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "These two distances are equal in length, so we are done. \n" ); document.write( "

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