SOLUTION: Find the equation of the angle bisector of the acute angles formed by the lines x+3y=9 and 4x+y=8.

Question 1011461: Find the equation of the angle bisector of the acute angles formed by the lines x+3y=9 and 4x+y=8.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the equation of the angle bisector of the acute angles formed by the lines x+3y=9 and 4x+y=8.
----------------
Find the intersection of the 2 lines.
x +3y=9
12x+3y=24 2nd eqn times 3
----------------- Subtract
-11x = -15
x = 15/11
y = 3 - x/3 = 28/11
-------------
--> (15/11,28/11) is the intersection
==================================
Use two lines thru the Origin with the same slopes to find the slope of the bisector.
x+3y=9 --> m1 = -1/3
4x+y=8.--> m2 = -4
---
The lines thru the Origin are:
y = -x/3 and y = -4x
----
The 2 slopes are -1/3 and -4
The slope is the tangent of the angle with the x-axis.
atan(-1/3) =~ -18.4349 degs
atan(-4) =~ -75.9638 degs
The average =~ -47.1993 degs
The slope of the bisector = tan(-47.1993) = -1.08
------
Use y-y1 = m*(x-x1)
y - 28/11 = -1.08*(x - 15/11)

RELATED QUESTIONS
Find the Equation of the angle bisector of the acute angles formed by the lines X+3y=9... (answered by KMST)

Find the equation of the bisector of the pair of acute angles formed by the lines 4x-3y=... (answered by melledwyer,Alan3354)

please help me answer this: Find the equation of the bisector of the pair of acute... (answered by rothauserc)

what is the equation of the line bisector of the acute angle formed by the intersection... (answered by KMST)

Find the equation of the bisector of the acute angles and also the equation of the... (answered by Alan3354)

Find the equation of the bisector of the acute angles and also the equation of the... (answered by robertb)

find the equation of the bisector of the acute angles and also the equation of the obtuse (answered by Alan3354)

Find the equation of the line bisecting the acute angles formed between lines X+7y=6... (answered by Fombitz)

Find the equation of the bisector of the obtuse angle formed by the lines x + 2y - 3 = 0... (answered by Edwin McCravy,Theo)