SOLUTION: Find an equations of the lines bisecting the angles from 3x – 4y – 2 = 0 to
4x – 3y + 4 = 0.
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Question 1042149: Find an equations of the lines bisecting the angles from 3x – 4y – 2 = 0 to
4x – 3y + 4 = 0.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I presume you mean you want equations of the lines that bisect the angles formed by the intersection of the two given lines. It is either that or I have no idea how to interpret what you wrote.
Solve the 2X2 system of equations to find the point of intersection of the two lines. It will be convenient to express the values of the coordinates as improper fractions.
Calculate the slope of each of the lines; for the sake of discussion, I will refer to the two slopes as 
and 
.
The angle between the first line and a horizontal line that passes through the intersection determined earlier is given by )
and the angle between the second line and that horizontal line is given by )
. The angle between the horizontal line and one of the bisectors of the angles formed by the intersection of the lines is the average of the two angles just calculated, and the tangent of that angle is the slope of the bisector, 
. So,
\ +\ \arctan(m_2)}{2}\right))
Then an equation of one of the lines that bisect one pair of the angles between the two given lines can be derived using the Point-Slope form:
 )
presuming )
are the coordinates of the point determined in the first part of this procedure.
Since the bisector of one pair of vertical angles is perpendicular to the bisector of the other pair, all we need for the equation of the other bisector is:
 )
John
My calculator said it, I believe it, that settles it
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