Question

Coloured strips are printed on a transparent sheet as shown below. The bottom half of this sheet is folded backwards along the PQ axis to form a semi-circle. Which of the option(s) will be a part of the resultant semi-circle?

• A. Fig A
• B. Fig B
• C. Fig C
• D. Fig D

Hint:

When dealing with transparent overlays, establish the invariant axis first. Here, the vertical columns never change order. Once you determine the upward reflection sequence of the horizontal rows, you can instantly eliminate any option with inverted row colors.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given a flat transparent sheet divided into two halves by a horizontal fold axis PQ. The upper half features a vertical array of colored stripes, while the lower half features a horizontal array of colored stripes. We must visualize the overlapping grid pattern formed when the lower half is folded backwards across PQ.

Step 2: Key Formula or Approach:
To determine the correct color intersections in the 2x2 grid options:

• Vertical stripes maintain their exact horizontal positions and left-to-right color sequence.

• Folding backwards across a horizontal line reflects the horizontal stripes vertically upward.

• The horizontal stripe situated immediately below the PQ line will end up immediately above the PQ line (at the bottom of the semi-circle). The stripe furthest below PQ reflects to the highest position.


Step 3: Detailed Explanation:

• Let us map the vertical stripes moving outward from the central vertical Red stripe:
- Center: Red
- 1st step outward: Purple
- 2nd step outward: Blue
- 3rd step outward: Green
- 4th step outward: Yellow
- Consequently, on the left side of the vertical center, the stripes run from left to right as: Green \(\to\) Blue \(\to\) Purple \(\to\) Red.
- On the right side of the vertical center, they run from left to right as: Red \(\to\) Purple \(\to\) Blue \(\to\) Green.

• Let us map the horizontal stripes moving downward from the PQ line before folding:
- 1st stripe below PQ: Blue
- 2nd stripe below PQ: Purple
- 3rd stripe below PQ: Green
- 4th stripe below PQ: Yellow

• Upon reflecting vertically across PQ:
- The Blue horizontal stripe sits at the absolute bottom of the semi-circle.
- The Purple horizontal stripe sits directly above the Blue stripe.
- The Green horizontal strip sits directly above the Purple stripe.
- Therefore, any localized vertical sample of two adjacent horizontal stripes must show Purple on the bottom and Green on the top.

• Let us evaluate the options:
-

Option C: Displays a vertical Green stripe on the left and a vertical Blue stripe on the right. Their overlapping rows show a horizontal Purple stripe at the bottom and a Green stripe at the top. This perfectly matches the left half of the transparent sheet.
-

Option D: Displays a vertical Blue stripe on the left and a vertical Green stripe on the right. The horizontal rows again correctly show Purple on the bottom and Green on the top. This perfectly matches the right half of the transparent sheet.


Step 4: Final Answer:
Options (C) and (D) correctly represent sections of the resultant folded semi-circle.