+0  
 
0
5
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avatar+1791 

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$

 

Note: The point $(x,y)$ lies in the first quadrant if both $x$ and $y$ are positive.

 Mar 24, 2024
 #1
avatar+128794 
+1

slope PQ =  -1 /  tan [ (arctan (4)  + arctan (5) ) / 2 ]    =  [19 - sqrt 442 ] /  9  ≈  -.225

 

cool cool cool

 Mar 24, 2024

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