Given two lines, one with a slope of 13/9 and the other with a slope of 1/3, find the slope of the bisector.
According to Wolfram (a very authoritative site), to find this slope, use this formula:
slope = [ m1·m2 - 1 + sqrt{ (m12 + 1)·(m22 + 1) } ] / ( m1 + m2 )
For this problem: m1 = 13/9 and m2 = 1/3.
Putting these numbers into the formula:
numerator = [ (13/9)·(1/3) - 1 + sqrt{ ( (13/9)2 + 1 ) · ( (1/3)2 + 1 ) } = [13/27 - 1 + 50/27 ] = 36/27
denominator = ( 13/9 + 1/3 ) = 16/9
slope = ( 36/27) / ( 16/9 ) = 3/4.
I checked these out using inverse tangent for 13/9, 1/3, and 3/4 and found that they work.