document.write( "Question 152310: 26.) The midpoint of the line segment joining a moving point to (6,0) is on the line y=x. Find the equation of its locus.
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\n" ); document.write( "\n" ); document.write( "This is a question that comes with the answer but I don't know how to solve for it. I tried using the midpoint formula but the answer is either x+y-6=0 or x-y-6=0. I don't know how to solve for this kind of problem... \n" ); document.write( "

Algebra.Com's Answer #113242 by Edwin McCravy(20055) $\"\"$ $\"About$

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26.) The midpoint of the line segment joining a moving point to (6,0) is on the line y=x. Find the equation of its locus.
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document.write( "Graph the line :\r\n" );
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document.write( "Call point (6,0) the point R.\r\n" );
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document.write( "Draw an arbitrary line from point R(6,0), crossing the\r\n" );
document.write( "line  at point M, and extending to P so that MP\r\n" );
document.write( "equals RM. making M the midpoint of RP.  P is the moving\r\n" );
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document.write( "Label the moving point P with the variable coordinates (x,y) \r\n" );
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document.write( "Since point M is the midpoint of the line segment RP, we use\r\n" );
document.write( "the midpoint formula to label M with the coordinates \r\n" );
document.write( "(,) or (,) \r\n" );
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document.write( "Now the point M(,) is on the line , so\r\n" );
document.write( "it must satisfy the equation , so we substitute that point \r\n" );
document.write( "into the equation  and we get:\r\n" );
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document.write( "Multiply both sides by 2:\r\n" );
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document.write( "That is equivalent to\r\n" );
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document.write( "To see the path of the moving point we draw the graph of\r\n" );
document.write( " in green\r\n" );
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document.write( "Edwin

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