The figure below shows a square sheet of paper being folded in two steps along…
2025
The figure below shows a square sheet of paper being folded in two steps along the dotted lines, and a pattern being punched on the folded sheet, as shown in the third box. Select the option figure that shows how the pattern will appear when the paper is unfolded completely.
Attempted by 42 students.
Show answer & explanation
Concept: When a sheet is folded along a line and a mark is added on the folded (reduced) layers, opening the sheet reflects that mark across every fold line used - each fold line acts as a mirror axis, so the fully unfolded pattern is symmetric about all the fold lines used.
Application:
The sheet is first folded along the horizontal dotted line, then along the vertical dotted line, and the mark is added on the small folded square that remains.
Undo the folds in reverse order. Unfolding the vertical fold reflects the mark across the vertical line, producing two mirrored copies side by side.
Unfolding the horizontal fold next reflects that two-copy shape across the horizontal line, producing four mirrored copies arranged symmetrically about both the horizontal and vertical mid-lines.
Cross-check: the resulting outline must be symmetric under both a left-right flip and a top-bottom flip, since it was built from two perpendicular folds - the bowtie-shaped figure with matching points above and below the centre line satisfies both symmetries at once, while the other figures either add extra shapes, keep only one axis of symmetry, or clip the corners instead of the edge.