document.write( "Question 1123947: ABCD is a rectangle/ The coordinates of A and B are (1,4) and (5,2) respsectively. The x-coordinate of D is -2. Find:
\n" ); document.write( "a) the equation of AD
\n" ); document.write( "b) the y-coordinate of D
\n" ); document.write( "c) the coordinates of C
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Algebra.Com's Answer #740322 by MathLover1(20855)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "\"ABCD\" is a rectangle\r
\n" ); document.write( "\n" ); document.write( "The coordinates of \"A\" and \"B\" are (\"1\",\"4\") and (\"5\",\"2\") respectively. \r
\n" ); document.write( "\n" ); document.write( "The x-coordinate of \"D\" is \"-2\". -> \"D\" is at (\"-2\",\"y\")\r
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\n" ); document.write( "\n" ); document.write( "Find:\r
\n" ); document.write( "\n" ); document.write( "a) the equation of \"AD\"\r
\n" ); document.write( "\n" ); document.write( "we will first find a slope of line that contais\"AB\", a line that is perpendicular to the line that contains \"AD\" :\r
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\n" ); document.write( "\n" ); document.write( "use given points (\"1\",\"4\") and (\"5\",\"2\") to find slope \"m\"\r
\n" ); document.write( "\n" ); document.write( "\"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r
\n" ); document.write( "\n" ); document.write( "\"m=%282-4%29%2F%285-1%29\"\r
\n" ); document.write( "\n" ); document.write( " will have a slope ...use given point that lie on AB (\"1\",\"4\") (\r
\n" ); document.write( "\n" ); document.write( "\"4=2%2A1%2Bb\"
\n" ); document.write( "\"4-2=b\"
\n" ); document.write( "\"b=2\"\r
\n" ); document.write( "\n" ); document.write( "and, your equation o the line {{AD}}} is: \"y=2x%2B2\"\r
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\n" ); document.write( "\n" ); document.write( "b) the y-coordinate of \"D\"\r
\n" ); document.write( "\n" ); document.write( "to find it, use \"y=2%29x%2B2\" and (\"-2\",\"y\")
\n" ); document.write( "\"y=2%28-2%29%2B2\"
\n" ); document.write( "\"y=-4%2B2\"
\n" ); document.write( "\"y=-2\"
\n" ); document.write( "so,\"D\" is at (\"-2\",\"-2\")\r
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\n" ); document.write( "\n" ); document.write( "c) the coordinates of \"C+\"\r
\n" ); document.write( "\n" ); document.write( "point \"C+\" is intersection point o the line \"DC\" and \"BC\"\r
\n" ); document.write( "\n" ); document.write( "since the line \"DC\" is parallel to the line \"AB\", they have same slope\r
\n" ); document.write( "\n" ); document.write( "\"m=-1%2F2\"\r
\n" ); document.write( "\n" ); document.write( "equation of the line \"DC\" is:\r
\n" ); document.write( "\n" ); document.write( "\"y=-%281%2F2%29x%2Bb\"....use point \"D\" which is at (\"-2\",\"-2\")\r
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\n" ); document.write( "\n" ); document.write( "\"-2=-%281%2F2%29%28-2%29%2Bb\"\r
\n" ); document.write( "\n" ); document.write( "\"-2=1%2Bb\"\r
\n" ); document.write( "\n" ); document.write( "\"-2-1=b\"\r
\n" ); document.write( "\n" ); document.write( "\"b=-3\"\r
\n" ); document.write( "\n" ); document.write( "\"y=-%281%2F2%29x-3\".....eq.1\r
\n" ); document.write( "\n" ); document.write( "and equation of \"AD\" has a slope \"m=2\" and is parallel to \"BC\"\r
\n" ); document.write( "\n" ); document.write( "so,equation of the line \"BC\" is:
\n" ); document.write( "\"y=2x%2Bb\"....use point \"B\" which is at (\"5\",\"2\")\r
\n" ); document.write( "\n" ); document.write( "\"2=2%2A5%2Bb\"\r
\n" ); document.write( "\n" ); document.write( "\"2-10=b\"\r
\n" ); document.write( "\n" ); document.write( "\"b=-8\"\r
\n" ); document.write( "\n" ); document.write( "and \"y=2x-8\".....eq.2\r
\n" ); document.write( "\n" ); document.write( "from eq.1 and eq.2 we have\r
\n" ); document.write( "\n" ); document.write( "\"2x-8=-%281%2F2%29x-3\"\r
\n" ); document.write( "\n" ); document.write( "\"2x%2B%281%2F2%29x=8-3\"\r
\n" ); document.write( "\n" ); document.write( "\"2x%2Bx%2F2=5\"\r
\n" ); document.write( "\n" ); document.write( "\"4x%2Bx=10\"\r
\n" ); document.write( "\n" ); document.write( "\"5x=10\"\r
\n" ); document.write( "\n" ); document.write( "\"x=2\"
\n" ); document.write( "go to \"y=2x-8\".....eq.2, plug in \"x\"\r
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\n" ); document.write( "\n" ); document.write( " \"y=2%2A2-8\"
\n" ); document.write( " \"y=4-8\"
\n" ); document.write( " \"y=-4\"\r
\n" ); document.write( "\n" ); document.write( "so, point \"C+\" is at (\"2\",\"-4\")\r
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\n" ); document.write( "\n" ); document.write( "(\"1\",\"4\") and (\"5\",\"2\")\r
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