document.write( "Question 885759: If. A(-8;6),B,C and D(3;9) are vertices of a rhombus. The equation for AC is 3y=-x+10\r
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Algebra.Com's Answer #535438 by Edwin McCravy(20060) $\"\"$ $\"About$
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document.write( "The green line is the line 3y=-x+10\r\n" );
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document.write( "As you can see from the graphs below, there are two possible \r\n" );
document.write( "solutions for the rhombus.\r\n" );
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document.write( "There is a mistake in your problem, for as you see the line BD cannot\r\n" );
document.write( "possibly pass through the origin, yet the problem states:\r\n" );
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document.write( "\"Show that BD is 3x-y=0\"\r\n" );
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document.write( "But 3x-y=0 passes through the origin (0,0), so there is no way that\r\n" );
document.write( "3x-y=0 could be the equation of BD. \r\n" );
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document.write( "Let's find what the equation of BD really is.  \r\n" );
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document.write( "BD is parallel to AC and has the same slope.\r\n" );
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document.write( "AC has the equation  \r\n" );
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document.write( "Solving for y,  \r\n" );
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document.write( "thus the slope of AC and BD is \r\n" );
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document.write( "And BD passes through D(3,9)\r\n" );
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document.write( "Using the point-slope formula:\r\n" );
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document.write( "Multiply through by 3\r\n" );
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document.write( "{{-{x-3)}}} \r\n" );
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document.write( "{{-x+3}}}\r\n" );
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document.write( "This is correct equation for BD, not 3y-x=0.  \r\n" );
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document.write( "Now we must find the coordinates of the K, the intersection of the\r\n" );
document.write( "diagonals.  Since the diagonals of a parallellogram bisect each other,\r\n" );
document.write( "we only need to find the midpoint of one of the diagonals.  We will\r\n" );
document.write( "need to find the coordinates of C, and then K will be the midpoint of\r\n" );
document.write( "diagonal CD. \r\n" );
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document.write( "Since this is a rhombus, all sides must be equal.  So we find side \r\n" );
document.write( "AD using the distance formula:\r\n" );
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document.write( "So the length of all 4 sides is  \r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "Now we must solve this system of equations to find p and q,\r\n" );
document.write( "the coordinates of C\r\n" );
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document.write( "Solve the first equation for p, p = 10-3q\r\n" );
document.write( "Substitute in the second equation,\r\n" );
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document.write( "Divide through by 10\r\n" );
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document.write( "Solve by the quadratic formula and get\r\n" );
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document.write( "using the +, substitute in\r\n" );
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document.write( "So point C in the graph on the right above is\r\n" );
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document.write( "using the -, substitute in\r\n" );
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document.write( "So point C in the graph on the left above is\r\n" );
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document.write( "Now we will find the midpoint of CD which will be K,\r\n" );
document.write( "where the two diagonals intersect.\r\n" );
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document.write( "We will find K for the graph on the left.\r\n" );
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document.write( "For the graph on the left\r\n" );
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document.write( " and D(3,9)\r\n" );
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document.write( "Using the midpoint formula:\r\n" );
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document.write( "Midpoint = \r\n" );
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document.write( "Midpoint = \r\n" );
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document.write( "Midpoint = \r\n" );
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document.write( "For the graph on the right\r\n" );
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document.write( " and D(3,9)\r\n" );
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document.write( "Using the midpoint formula:\r\n" );
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document.write( "Midpoint = \r\n" );
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document.write( "Midpoint = \r\n" );
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document.write( "Midpoint = \r\n" );
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document.write( "Edwin
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