On a square transparent sheet, a pattern is shown. Determine how this pattern…
2024
On a square transparent sheet, a pattern is shown. Determine how this pattern will appear once the sheet is folded along the dotted line.

Attempted by 50 students.
Show answer & explanation
Concept
When a transparent sheet is folded along a straight line, the part lying on one side of that line reflects exactly onto the other side. Because the sheet is transparent, the folded view shows the portion that stayed in place together with the mirror image of the portion that got folded over, and the two pieces are joined at the very same points where the pattern originally crossed the fold line.
Applying it here
The given pattern crosses the dotted line: a rounded arch sits above the line, and a pointed tail hangs below it, meeting the line at the same two points where the arch's ends touch it. Folding the lower tail up across the line reflects it into an upward-pointing angular peak of the same base width, with its height equal to how far the tail originally hung below the line.
Overlaying this reflected peak on the arch that already sits above the line gives a single figure: the rounded arch stays as the outer boundary, ending exactly at the two points on the fold line, and the reflected peak rises inside it, anchored at those same two points.
Cross-check
Since the arch and the tail are one continuous outline, they must share identical base points on the fold line. Reflecting the tail therefore produces a peak whose base coincides exactly with the arch's base and whose height matches the tail's own depth — the arch must not extend into a closed loop below the line, the peak must not rise taller than the arch, and the peak must remain anchored at the arch's own base points rather than floating separately inside it.
