SOLUTION: Find the equation of the bisector of the pair of acute angles formed by the lines 4x-3y= 8 and 2x+y=4

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 Click here to see ALL problems on Miscellaneous Word Problems Question 374054: Find the equation of the bisector of the pair of acute angles formed by the lines 4x-3y= 8 and 2x+y=4Found 2 solutions by melledwyer, Alan3354:Answer by melledwyer(2)   (Show Source): Answer by Alan3354(30959)   (Show Source): You can put this solution on YOUR website!Find the intersection of the 2 lines, = (2,0) ----------- Find the slope of the 2 lines: 4x-3y = 8 m1 = 4/3 2x+y = 4 m2 = -2 ------------- The slope is the arctan of the angle the line makes with the x-axis arctan(4/3) =~ 53.13º arctan(-2) =~ -63.435º The angle between them is 116.565º (in Quad 1), so the acute angles are 83.435º The bisector makes and angle of 53.15 + (83.435)/2 = 84.8675º with the x-axis Its slope = tan(84.8675) = 11.133 --------------------- Use y = mx + b and the point (2,0) 0 = 2*11.133 + b b = -22.266 Equation is y = 11.133x - 22.266