The point $P(1,2,3)$ is reflected in the $x-y$ plane, Then its image $Q$ is rotated by $180^\circ$ about the $x$ axis to produce $R$, finally $R$ is translated in the direction of positive $y$ axis through the distance $d$ to produce $S(1,3,3)$. Then $d$ is
Try: Coordinate of $Q$ is $(1,2,-3)$. Now i did not understand How can i rotate $180^\circ$ about $x$ axis. Could some help me, thanks
If you rotate about $x$-axis, you keep the $x$-value fixed, and flip the sign of the $y$ and $z$ coordinate.
Hence $R$ is $(1, -2, 3)$.
Hopefully you can compute $d$ from here.