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The line $y = mx$ bisects the angle between the two lines shown below.  Find $m$.

 

The two lines are y = x and y = 2x.

 Jan 2, 2024
 #1
avatar+129316 
+1

y= x

y =2x

 

We can  find  m thusly 

 

  m  =  tan [ (arctan(slope of one  line) + arctan(slope of second line) / 2  ]  

 

  =      tan ([ arctan (2)   + arctan(1)] /  2)   ≈ 1.387

 

 

cool cool cool

 Jan 3, 2024
edited by CPhill  Jan 3, 2024

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