A line segment of length 5 lies along the number line initially between 1 and 6 .

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-057.jpg?height=103&width=916&top_left_y=1195&top_left_x=564)

The line segment is rotated $180^{\circ}$ about the point at 2 . The resulting line segment lies between -2 and 3 . This segment is then rotated $180^{\circ}$ about the point at 1 . The resulting line segment lies between
(A) -2 and 3
(B) -1 and 4
(C) 0 and 5
(D) -3 and 2
(E) -4 and 1

Part B: Each correct answer is worth 6.
After the first rotation, the line segment lies between -2 and 3 .

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-112.jpg?height=95&width=930&top_left_y=1275&top_left_x=652)

The line segment is now to be rotated about the point at 1 .

Since the right endpoint of the segment is 2 units to the right of 1 before the rotation, then the left endpoint of the segment will be 2 units to the left of 1 after the rotation.

Thus, the left endpoint will be at -1 .

Since the line segment has length 5 , then its right endpoint will be at $-1+5=4$.

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-112.jpg?height=106&width=916&top_left_y=1720&top_left_x=664)

Thus, the line segment lies between -1 and 4 .

ANSWER: (B)