The word "stop" starts in the position shown in the diagram to the right. It is then rotated $180^{\circ}$ clockwise about the origin, $O$, and this result is then reflected in the $x$-axis. Which of the following represents the final image?

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-090.jpg?height=312&width=331&top_left_y=367&top_left_x=1339)
(A)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-090.jpg?height=217&width=201&top_left_y=694&top_left_x=515)
(B)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-090.jpg?height=219&width=203&top_left_y=693&top_left_x=755)
(C)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-090.jpg?height=219&width=217&top_left_y=693&top_left_x=997)
(D)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-090.jpg?height=216&width=203&top_left_y=697&top_left_x=1248)
(E)

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-090.jpg?height=216&width=200&top_left_y=697&top_left_x=1491)

Part C: Each correct answer is worth 8.
The word "stop" starts in the position shown in the diagram to the right. It is then rotated 180r clockwise about the origin, $O$, and this result is then reflected in the $x$-axis. Which of the following represents the final image?
(A)

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-387.jpg?height=272&width=241&top_left_y=1062&top_left_x=411)
(B)

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-387.jpg?height=271&width=250&top_left_y=1065&top_left_x=707)
(C)

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-387.jpg?height=268&width=263&top_left_y=1064&top_left_x=996)
(D)

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-387.jpg?height=272&width=247&top_left_y=1062&top_left_x=1297)
(E)

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-387.jpg?height=260&width=258&top_left_y=1071&top_left_x=1584)

## Solution

If we start by rotating by $180^{\circ}$ and then reflecting that image, we would get the following:

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-387.jpg?height=385&width=393&top_left_y=1518&top_left_x=606)

Rotation of $180^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-387.jpg?height=385&width=377&top_left_y=1515&top_left_x=1167)

Reflection in $x$-axis

ANSWER: (E)

## Part C