document.write( "Question 550393: The co-ordinates of the vertex A of a square ABCD are (1,2) and the equation of the diagonal BD is x+2y=10.Find the equation of the other diagonal and the co-ordinates of centre of the square.pls...help me \n" ); document.write( "
Algebra.Com's Answer #358989 by KMST(5328)\"\" \"About 
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The diagonals of a square are perpendicular, so you need to find the equation of the line that contains AC, perpendicular to \"x%2B2y=10\", and passing through A (1, 2).
\n" ); document.write( "The line that contains BD is described by the equivalent equations
\n" ); document.write( "\"x%2B2y=10\" --> \"2y=-x%2B10\" --> \"y=%28-1%2F2%29x%2B5\".
\n" ); document.write( "So the slope of that line is \"-1%2F2\".
\n" ); document.write( "The slope of all lines perpendicular to that line is
\n" ); document.write( "\"%28-1%29%2F%28-1%2F2%29=2\".
\n" ); document.write( "The equation of a line with slope 2 passing through point (1, 2) is
\n" ); document.write( "\"y-2=2%28x-1%29\" --> \"y-2=2x-2\" --> \"y=2x\".
\n" ); document.write( "So the equations of the two diagonals are
\n" ); document.write( "\"y=2x\" for the line containing AC, and
\n" ); document.write( "\"x%2B2y=10\" for the line containing BD.
\n" ); document.write( "They meet at the center of the square. The coordinates of the center of the square can be found by solving the system formed by the to equations.
\n" ); document.write( "Substituting \"y=2x\" in \"x%2B2y=10\"
\n" ); document.write( "\"x%2B2%282x%29=10\" -->\"x%2B4x=10\" -->\"5x=10\" -->\"x=2\"
\n" ); document.write( "Then, \"y=2x=2%2A2=4\"
\n" ); document.write( "The center of the square is (2,4).
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