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avatar+1808 

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.

 Jul 30, 2024
 #1
avatar+1892 
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mmm...let's see....

We simply have

\(slope PQ = -1 / tan [ (arctan (4) + arctan (5) ) / 2 ] = [19 - \sqrt{ 442} ] / 9 ≈ -0.225 \)

 

So I think the answer is -0.225. 

https://web2.0calc.com/questions/help-with-coordinates_36

 

Thanks! :)

 Jul 30, 2024
edited by NotThatSmart  Jul 30, 2024

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