document.write( "Question 1180859: Given two lines 2x - y - 1 = 0 …eq. 1and 3x + y - 4= 0 …eq. 2, and point A (0, 4) lying on eq. 2, find the equation of the line which is symmetric to eq. 2 with respect to eq. 1\r
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Algebra.Com's Answer #811105 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Get some graph paper and plot the lines:\r\n" );
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document.write( "The red line is the line 2x-y-1=0, eq.1\r\n" );
document.write( "The blue line is the line 3x+y-4=0, eq.2\r\n" );
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document.write( "They cross at the point (1,1)\r\n" );
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document.write( "Notice that to get from the point where they cross (1,1)\r\n" );
document.write( "we have to go left 1 unit and then up 3 units.  That's\r\n" );
document.write( "indicated by the green lines:\r\n" );
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document.write( "Now this time starting at (1,1) and go right as many units\r\n" );
document.write( "as you went up before, and up as many units as you went\r\n" );
document.write( "left before, like the other green lines below:\r\n" );
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document.write( "You see that you ended up at the point (4,2).\r\n" );
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document.write( "Now draw a line through (1,1) and (4,2), like this black\r\n" );
document.write( "line below:\r\n" );
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document.write( "That black line is the line which is symmetric to eq. 2 with\r\n" );
document.write( "respect to eq. 1. \r\n" );
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document.write( "We find its equation.  It goes through (1,1) and (4,2).\r\n" );
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document.write( "We use the slope formula:\r\n" );
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document.write( "Then we use the point-slope form:\r\n" );
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document.write( "Multiply through by 3\r\n" );
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document.write( "or, multiplying by -1\r\n" );
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document.write( "  <-- the equation of the black line.\r\n" );
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document.write( "Edwin

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