document.write( "Question 1011461: Find the equation of the angle bisector of the acute angles formed by the lines x+3y=9 and 4x+y=8. \n" ); document.write( "

Algebra.Com's Answer #627136 by Alan3354(69443) $\"\"$ $\"About$

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Find the equation of the angle bisector of the acute angles formed by the lines x+3y=9 and 4x+y=8.
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\n" ); document.write( "Find the intersection of the 2 lines.
\n" ); document.write( " x +3y=9
\n" ); document.write( "12x+3y=24 2nd eqn times 3
\n" ); document.write( "----------------- Subtract
\n" ); document.write( "-11x = -15
\n" ); document.write( "x = 15/11
\n" ); document.write( "y = 3 - x/3 = 28/11
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\n" ); document.write( "--> (15/11,28/11) is the intersection
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\n" ); document.write( "Use two lines thru the Origin with the same slopes to find the slope of the bisector.
\n" ); document.write( "x+3y=9 --> m1 = -1/3
\n" ); document.write( "4x+y=8.--> m2 = -4
\n" ); document.write( "---
\n" ); document.write( "The lines thru the Origin are:
\n" ); document.write( "y = -x/3 and y = -4x
\n" ); document.write( "----
\n" ); document.write( "The 2 slopes are -1/3 and -4
\n" ); document.write( "The slope is the tangent of the angle with the x-axis.
\n" ); document.write( "atan(-1/3) =~ -18.4349 degs
\n" ); document.write( "atan(-4) =~ -75.9638 degs
\n" ); document.write( "The average =~ -47.1993 degs
\n" ); document.write( "The slope of the bisector = tan(-47.1993) = -1.08
\n" ); document.write( "------
\n" ); document.write( "Use y-y1 = m*(x-x1)
\n" ); document.write( "y - 28/11 = -1.08*(x - 15/11)
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