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Two black lines pass through the origin, as shown below.  If their slopes are \(2\) and \(5\), then find the slope of the red line that bisects the acute angle between these lines.

 

 Apr 20, 2022
 #1
avatar+2455 
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I answered a similar question here: https://web2.0calc.com/questions/coordinates_33120

 Apr 20, 2022
 #2
avatar+124598 
+1

We can find the slope thusly :

 

slope =  tan  [ (arctan (5)  + arctan(2) )  / 2 ]     =   (  9 + sqrt 130)  /  7   

 

 

cool cool cool

 Apr 20, 2022

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