Explore the distances from an interior point of a hexagon to its sides. What is the sum of these perpendicular distances?
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Adjust the size of the hexagon by moving points X and Y.
Drag point Q around within the figure. As Q is moved, the measurements from Q to each side will automatically adjust. Note that if Q is positioned such that the intersection with a side lies outside the hexagon, the segment and measurement will be removed.
Choose Trace Path of Q to trace the path of point Q as it is moved. To erase the path, click the red X in the lower right corner of the applet.
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Choose Trace Path. Then, slowly and carefully drag Q through the interior of the hexagon so that all six segments (AQ‑FQ) are visible. If any segments disappear, move back toward the interior so that they reappear.
- Describe the region through which Q can move so that none of the segments disappear.
- Explain why this happens.
- How is the region determined? Why does it have the shape it has?
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