document.write( "Question 896575: What are the coordinates of points Q and R where Q is on $\"+y=%281%2F2%29x-2+\"$ and R is on $\"+y=+-x%2B5+\"$ and a line is drawn from P to intersect with the lines so that P is the midpoint of QR and P(1,1) \n" ); document.write( "

Algebra.Com's Answer #543659 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "We let the x-component of Q be a, Then since Q is on the line\r\n" );
document.write( ", the y-component of Q is found by substituting\r\n" );
document.write( "a for x in  and get . So\r\n" );
document.write( "Q is the point Q(a,),\r\n" );
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document.write( "We let the x-component of R be b, Then since R is on the line\r\n" );
document.write( ", the y-component of R is found by substituting\r\n" );
document.write( "b for x in  and get . So\r\n" );
document.write( "R is the point R(b,-b+5)\r\n" );
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document.write( "We are told that P(1,1) is the midpoint of QR.  We use the\r\n" );
document.write( "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( "So we equate those coordinates to the coordinates of P(1,1).\r\n" );
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document.write( "Equating the x-coordinates of P\r\n" );
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document.write( "Equating the y-coordinates of P\r\n" );
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document.write( "Multiply through by 2:\r\n" );
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document.write( "So we solve the system by substitution or elimination:\r\n" );
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document.write( "Solve the first for a=2-b\r\n" );
document.write( "Substitute in the second equation:\r\n" );
document.write( "(2-b)-2b=-2\r\n" );
document.write( "  2-b-2b=-2\r\n" );
document.write( "    2-3b=-2\r\n" );
document.write( "     -3b=-4\r\n" );
document.write( "       b=\r\n" );
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document.write( "a=2-b\r\n" );
document.write( "a=2-\r\n" );
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document.write( "So the point  becomes:\r\n" );
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document.write( "So the point R(b,-b+5) becomes:\r\n" );
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document.write( "Edwin

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