The point (5, −3) is first reflected in the line $y=x$, and the image obtained is then reflected in the $x$-axis. What are the coordinates of the final image?

Reflection in $y=x$ swaps the coordinates: (5, −3) becomes (−3, 5). Reflection in the $x$-axis changes the sign of the $y$-coordinate: (−3, 5) becomes (−3, −5). Stopping after the first step gives (−3, 5), which is the trap.