document.write( "Question 1173692: Quadrilateral KLMN has vertices K(2,3), L(7,3), M(4,7), and N (-1,7). Prove by means of coordinate geometry that KLMN is a rhombus. \n" ); document.write( "

Algebra.Com's Answer #798991 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Quadrilateral KLMN has vertices K(2,3), L(7,3), M(4,7), and N (-1,7). Prove by means of coordinate geometry that KLMN is a rhombus.
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document.write( "Looking at the coordinates of points, you may see that \r\n" );
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document.write( "    - the segment KL is horizontal  (y= 3)  having the length of 7-2 = 5;\r\n" );
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document.write( "    - the segment MN is horizontal  (y= 7)  having the length of 4-(-1) = 5.\r\n" );
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document.write( "It is just enough to conclude that the quadrilateral KLMN is a parallelogram.\r\n" );
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document.write( "Next, the length of the segment  KN is   =  = 5  and is equal to that of segment KL.\r\n" );
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document.write( "It is just enough to conclude that the parallelogram KLMN  is a rhombus.\r\n" );
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