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Problem 80

Geometry Difficulty 1.2 Find the answer CEMC Fermat · Canada · 2021

A square piece of paper has a dot in its top right corner and is lying on a table. The square is folded along its diagonal, then rotated 9090^\circ clockwise about its centre, and then finally unfolded, as shown.

The resulting figure is





A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

We draw an unshaded dot to represent the location of the dot when it is on the other side of the sheet of paper being shown. Therefore, the dot moves as follows:

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It is worth noting that folding and unfolding the paper have no net effect on the figure. Thus, the resulting figure can be determined by rotating the original figure by 9090^\circ clockwise.

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