SOLUTION: Find the equation of the bisector of the acute angles and also the equation of the bisector of the obtuse angles formed by the lines 7x − 24y = 8 and 3x + 4y = 12.

Question 1189505: Find the equation of the bisector of the acute angles and also the equation of the bisector of
the obtuse angles formed by the lines
7x − 24y = 8
and
3x + 4y = 12.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the equation of the bisector of the acute angles and also the equation of the bisector of
the obtuse angles formed by the lines
7x − 24y = 8
and
3x + 4y = 12.
-----------------------
Find the slope of each line, and the intersection:
L1: 7x − 24y = 8 - m1 = 7/24
L2: 3x + 4y = 12 - m2 = -3/4
==========
7x − 24y = 8
18x + 24y = 72
---------------------------- Add
25x = 80
x = 16/5
y = 3/5
Intersection (16/5,3/5)
==========================================
The slope is the tangent of the angle with the x-axis.
L1: Angle1 = 16.26 degs
l2: Angle2 = -36.87 degs
(16.26 - 36.87)/2 = -10.3 degs
Slope of bisector = tan(-10.3) = -0.181818... = -2/11
y-0.6 = (-2/11)*(x - 3.2) is the bisector of the acute angle
=============
The slope of the other bisector is the negative inverse, = 11/2
y-0.6 = (11/2)*(x - 3.2) is the bisector of the obtuse angle

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