+900 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.
+15070 Compute the slope of line segment ¯PQ.
Let ¯OQ=¯OP=5fc(x)=+√52−x2foq(x)=5xfop(x)=4x
√25−x2=5x25−x2=25x2xq=√2526=0.9806yq=√2526⋅5=4.903√25−x2=4xxp=√2517=1.2127yp=√2517⋅4=4.8507
mPQ=yq−ypxq−xp=4.9029−4.85070.9806−1.2127mPQ=−0.2249The slope of line segment ¯PQ is −0.2249.
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