SOLUTION: An acute angle is formed by two lines of slopes (1/2) and (2/11). What is the slope of the line which bisects the angle?

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Question 1145128: An acute angle is formed by two lines of slopes (1/2) and (2/11). What is the slope of the line which bisects the angle?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
The given slopes are the tangent values of corresponding angles.


Thus we have  tan(a) =   for one angle, "a", and  tan(b) =   for the other angle, "b".


They ask you about  .


Using well known formulas of Trigonometry,


     =  =  =  =  =  =  = .


The last step is to use the formula for  tan(c/2) via  tan(c)


     = .


When you apply it, you will get the ANSWER 


     =  =  =  =  = .


According to the condition, you may use the sign " + " at sqrt instead of " +/- ".


ANSWER.  The slope is  .


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
An acute angle is formed by two lines of slopes (1/2) and (2/11). What is the slope of the line which bisects the angle?
-----------------
Use the Origin as a point on both lines.
---> y = x/2 and y = 2x/11
------
Plot the points A(2,1) for slope 1/2 and B(11,2) for slope 2/11.
Find a point C the same distance from the Origin as B on the line y = x/2
distance to B = 5sqrt(5)
distance to A = sqrt(5)
---> point C is 5 times point A = (10,5)
-----------
Find the midpoint of BC = (10.5,3.5)
Slope = y/x = 1/3
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