I know the coordinates of points E and Q, so I know their euclidean distance L. I'm looking for the point W with coordinates (a,b) related to other known values?
One spot and distance known, Second spot unknown
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analytic-geometry
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0Assume the $E$ is the origin, for a moment. $\vec{EQ}=\binom{x}{y}=L\binom{\sin \theta}{\cos \theta}$. Then use vector addition: $\vec{EW}=\vec{EQ}+\vec{QW}$. If $E$ is not the origin, shift the result by $\vec{E}= \binom{e_1}{e_2}$. (all assuming $\theta$ is also known...) – 2012-04-16
1 Answers
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I'll assume you know $\theta$, the coordinates $(x,y)$ of $Q$, and $r$. The angle of rotation from a vertical line through $Q$ to $\overline{QW}$ is also $\theta$, so if we take the point that is $r$ above $Q$ and rotate it by $\theta$ about $Q$, we'll get $W$. That means $W=(a,b)=(x-r\sin\theta,y+r\cos\theta).$