document.write( "Question 1179468: The vertices of a kite are A (-3,1), B(0,5), C(4,2) and D(2, -9). \r
\n" ); document.write( "\n" ); document.write( "Determine the lengths of the four sides of the kite. What do you notice? \r
\n" ); document.write( "\n" ); document.write( "Determine the slopes of the diagonals (from one corner to the other corner) \r
\n" ); document.write( "\n" ); document.write( "What do you notice? \r
\n" ); document.write( "\n" ); document.write( "Find the midpoint of the diagonal AC. \r
\n" ); document.write( "\n" ); document.write( "Find the equation of the diagonal BD. \r
\n" ); document.write( "\n" ); document.write( "Show the midpoint of AC lies on the equation of a line though BD. \r
\n" ); document.write( "\n" ); document.write( "Analyze the previous calculations and list as many properties of a kite as you can.
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Algebra.Com's Answer #809039 by MathLover1(20850)\"\" \"About 
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\n" ); document.write( "The vertices of a kite are \r
\n" ); document.write( "\n" ); document.write( "A (\"-3\",\"1\")
\n" ); document.write( "B(\"0\",\"5\")
\n" ); document.write( "C(\"4\",\"2\")
\n" ); document.write( "D(\"2\",\"+-9\")\r
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\n" ); document.write( "\n" ); document.write( "Determine the lengths of the four sides of the kite. What do you notice?\r
\n" ); document.write( "\n" ); document.write( "the length of \"AB\" is:\r
\n" ); document.write( "\n" ); document.write( "\"AB=sqrt%28%280-%28-3%29%29%5E2%2B%285-1%29%5E2%29\"
\n" ); document.write( "\"AB=sqrt%283%5E2%2B4%5E2%29\"
\n" ); document.write( "\"AB=sqrt%2825%29\"
\n" ); document.write( "\"AB=5\"\r
\n" ); document.write( "\n" ); document.write( "the length of \"BC\" is:\r
\n" ); document.write( "\n" ); document.write( "\"BC=sqrt%28%284-0%29%5E2%2B%282-5%29%5E2%29\"
\n" ); document.write( "\"BC=sqrt%284%5E2%2B%28-3%29%5E2%29\"
\n" ); document.write( "\"BC=sqrt%2825%29\"
\n" ); document.write( "\"BC=5\"\r
\n" ); document.write( "\n" ); document.write( "the length of \"AD\" is:\r
\n" ); document.write( "\n" ); document.write( "\"AD=sqrt%28%282-%28-3%29%29%5E2%2B%28-9-1%29%5E2%29\"
\n" ); document.write( "\"AD=sqrt%285%5E2%2B%28-10%29%5E2%29\"
\n" ); document.write( "\"AD=sqrt%28125%29\"
\n" ); document.write( "\"AD=11.18\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the length of \"CD\" is:\r
\n" ); document.write( "\n" ); document.write( "\"CD=sqrt%28%282-4%29%5E2%2B%28-9-2%29%5E2%29\"
\n" ); document.write( "\"CD=sqrt%28%28-2%29%5E2%2B%28-11%29%5E2%29\"
\n" ); document.write( "\"CD=sqrt%28125%29\"
\n" ); document.write( "\"CD=11.18\"\r
\n" ); document.write( "\n" ); document.write( "I noticed that the length of \"AB\" is equal to the length of \"BC\", and the length of \"AD\" is equal to the length of \"CD\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Determine the slopes of the diagonals (from one corner to the other corner)
\n" ); document.write( "What do you notice?\r
\n" ); document.write( "\n" ); document.write( "the diagonal \"AC\" lie on a line that contains vertices \"A\" and \"C\"\r
\n" ); document.write( "\n" ); document.write( "slope is \"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\".......use A (\"-3\",\"1\") and C(\"4\",\"2\") \r
\n" ); document.write( "\n" ); document.write( "\"m=%282-1%29%2F%284-%28-3%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"m=1%2F%284%2B3%29\"
\n" ); document.write( "\"m=1%2F7\"\r
\n" ); document.write( "\n" ); document.write( "and \"BD\" lie on a line that contains vertices B(\"0\",\"5\") and D(\"2\",\"+-9\")\r
\n" ); document.write( "\n" ); document.write( "\"m=%28-9-5%29%2F%282-0%29\"
\n" ); document.write( "\"m=-14%2F2\"
\n" ); document.write( "\"m=-7\"\r
\n" ); document.write( "\n" ); document.write( "=>I have noticed that slopes are negative reciprocal to each other which means the diagonals are perpendicular to each other\r
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\n" ); document.write( "\n" ); document.write( "Find the midpoint of the diagonal AC.\r
\n" ); document.write( "\n" ); document.write( "A (\"-3\",\"1\") and C(\"4\",\"2\")\r
\n" ); document.write( "\n" ); document.write( "\"M\"=(\"%28-3%2B4%29%2F2\",\"%281%2B2%29%2F2\")
\n" ); document.write( "\"M\"=(\"1%2F2\",\"3%2F2\")\r
\n" ); document.write( "\n" ); document.write( "Find the equation of the diagonal \"BD\".\r
\n" ); document.write( "\n" ); document.write( "use \"m=-7\" and point B(\"0\",\"5\"), plug it in poit slope formula\r
\n" ); document.write( "\n" ); document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"
\n" ); document.write( "\"y-5=-7%28x-0%29\"
\n" ); document.write( "\"y-5=-7x\"
\n" ); document.write( "\"y=-7x%2B5\"\r
\n" ); document.write( "\n" ); document.write( "Show the midpoint of AC lies on the equation of a line though BD.\r
\n" ); document.write( "\n" ); document.write( "the midpoint of AC is \"M\"=(\"1%2F2\",\"3%2F2\")\r
\n" ); document.write( "\n" ); document.write( "\"y=-7x%2B5\"......substitute coordinates of the midpoint\r
\n" ); document.write( "\n" ); document.write( "\"3%2F2=-7%281%2F2%29%2B5\"\r
\n" ); document.write( "\n" ); document.write( "\"3%2F2=-7%2F2%2B10%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"3%2F2=3%2F2\"-> same, so the midpoint of \"AC\" lies on the equation of a line though \"BD\"\r
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