# Problem #865

 865 The point $P = (1,2,3)$ is reflected in the $xy$-plane, then its image $Q$ is rotated $180^\circ$ about the $x$-axis to produce $R$, and finally, $R$ is translated $5$ units in the positive-$y$ direction to produce $S$. What are the coordinates of $S$? $\textbf {(A) } (1,7, - 3) \qquad \textbf {(B) } ( - 1,7, - 3) \qquad \textbf {(C) } ( - 1, - 2,8) \qquad \textbf {(D) } ( - 1,3,3) \qquad \textbf {(E) } (1,3,3)$ This problem is copyrighted by the American Mathematics Competitions.
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