Algebra.Com's Answer #814763 by ikleyn(52790)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Find the locus of R if points P(2, -3) and Q(-2, 1) are vertices of triangle PQR and centroid of PQR lies on line 2x + 3y = 1.
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document.write( "Let R = (x,y).\r\n" );
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document.write( "Then the centroid of the triangle PQR has x-coordinate  = 1/3 of the sum x-coordinates of the vertices =  =  .\r\n" );
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document.write( " y-coordinate  = 1/3 of the sum y-coordinates of the vertices =  =  .\r\n" );
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document.write( "We want the centroid points (,) lie on the line 2x + 3y = 1.\r\n" );
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document.write( "So, we substitute for and for into this equation. We get then\r\n" );
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document.write( "  +  = 1.\r\n" );
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document.write( "It is EQUIVALENT to \r\n" );
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document.write( " + (y-2) = 1,\r\n" );
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document.write( " 2x + 3*(y-2) = 3,\r\n" );
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document.write( " 2x + 3y - 6 = 3\r\n" );
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document.write( " 2x + 3y = 9.\r\n" );
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document.write( "Thus the locus of points R(x,y) is the straight line 2x + 3y = 9. ANSWER\r\n" );
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document.write( "Solved and explained.\r
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