document.write( "Question 1188643: If A(3,6) and C(-1,2) are two vertices of a rhombus ABCD, then find the equation of straight line that lies along the diagonal BD. \n" ); document.write( "
Algebra.Com's Answer #819767 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "If A(3,6) and C(-1,2) are two vertices of a rhombus ABCD, then find the equation of straight line that lies along the diagonal BD.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                The STRATEGY\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(1)  First find an equation of the line AC;\r\n" );
document.write( "\r\n" );
document.write( "(2)  then find the midpoint of the segment AC;\r\n" );
document.write( "\r\n" );
document.write( "(3)  then find an equation of the perpendicular line passing through this midpoint.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                IMPLEMENTATION\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(1)  To find an equation of the line AC, first find its slope:  m = \"%282-6%29%2F%28-1-3%29\" = \"%28-4%29%2F%28-4%29\" = 1.\r\n" );
document.write( "\r\n" );
document.write( "     Hence, an equation of the line AC is  y-6 = 1*(x-3),  or  y-6 = x-3,  or  y - x = 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2)  The midpoint of the segment AC is (1,4)  (the mean values for each pair of co-named coordinates).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(3)  The perpendicular line to AC is  x + y = const = 1 + 4 = 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The sough equation is  x + y = 5  (or any other equation, equivalent to it . . . )\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );