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, 2014

Algebra Difficulty 1.4 Junior Find the answer Canada

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

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

Pick one

Solution

After the first rotation, the line segment lies between $-2$ and 3.

[[IMAGE0]]

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 $-1+5=4$ .

[[IMAGE1]]

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

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.