The sequence of folding a paper and the manner in which the folded paper is cut is shown in the following figures. How would this paper look when unfolded?

Correct Answer:

Step-by-Step Explanation:

Let's analyze the sequence of folding and cutting step-by-step:

1. First Fold (Horizontal/Lateral fold):
The rectangular sheet is folded in half from right to left. The right half is folded over the left half. The paper now has two layers on the left side.

2. Second Fold (Vertical fold):
The top half of the folded sheet is folded down to the bottom half. This leaves only the bottom-left quadrant (quarter) of the original sheet visible, consisting of four layers of paper.

3. The Cuts:
On this bottom-left quadrant, three shapes are cut out:

• A diamond (rhombus) on the left edge.
• A right-angled triangle on the right side, near the vertical fold line (the center line of the original sheet). Its vertical leg is on the right, its horizontal leg is at the bottom, and its hypotenuse slopes upwards from right to left.
• An arrow pointing upwards at the bottom.

4. Unfolding the Paper:
To see how the paper looks when unfolded, we reverse the folds in the opposite order:

1. Unfold upwards (Vertical Reflection):
   We reflect the cuts from the bottom-left quadrant into the top-left quadrant across the horizontal middle crease:
   • The diamond on the left remains a diamond on the left (symmetric).
   • The right-angled triangle is flipped vertically: its horizontal leg is now at the top, and its hypotenuse slopes downwards from right to left.
   • The upward-pointing arrow reflects to become a downward-pointing arrow at the top.


2. Unfold to the right (Horizontal Reflection):
   Now, we reflect the entire left half to the right half across the vertical center crease:
   • The diamonds on the outer left edge reflect to the outer right edge.
   • The right-angled triangles near the center crease reflect to the right side of the crease, creating a symmetrical mirror pattern facing each other.
   • The arrows on the left (one pointing up, one pointing down) reflect to the right side, maintaining their vertical orientations.

Combining all these reflections, the final unfolded sheet will display:

• Two upward-pointing arrows at the bottom.
• Two downward-pointing arrows at the top.
• Two diamonds on the far-left edge and two diamonds on the far-right edge.
• Four triangles arranged symmetrically around the center vertical line.