FERMAT 2014 Problem 10

Past Contests FERMAT 2014
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1

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

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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

Answer Choices
A. -2 and 3
B. -1 and 4
C. 0 and 5
D. -3 and 2
E. -4 and 1