Mirror and Water Images
About 7 min · Logical Reasoning · English
Time worked out from the lesson's 486 words at 150 words a minute, plus a minute for each question.
Mirror and water image problems test your ability to visualize how objects appear when reflected along different axes. In SOF IMO, you'll encounter letters, numbers, simple figures and sometimes clock faces that are reflected either horizontally (water image) or vertically (mirror image). These questions assess spatial reasoning—a skill critical not just for Olympiads but also for advanced geometry and real-world problem-solving.
Key ideas
- Mirror Image means reflection across a vertical axis (imagine a mirror held vertically to the right or left of the object). Left and right swap, but top and bottom stay the same.
- Water Image means reflection across a horizontal axis (imagine seeing the object's reflection in still water below it). Top and bottom swap, but left and right stay the same.
- Symmetric letters and numbers (like A, H, I, M, O, T, U, V, W, X, Y, 0, 8) look identical or nearly identical in their mirror images.
- Asymmetric letters (like B, C, D, E, F, G, J, K, L, N, P, Q, R, S, Z, 2, 3, 5, 6, 7, 9) change distinctly in a mirror image—these are where mistakes happen.
- For figures (triangles, arrows, shapes with curves), trace the outline mentally after flipping along the correct axis. Pay special attention to which side curves or points face.
Watch out for
- Confusing mirror and water images → Remember: mirror = vertical axis (left↔right swap); water = horizontal axis (top↔bottom swap). Underline the axis type in the question.
- Forgetting to reverse letter order in mirror image → A mirror image not only flips each letter but also reverses the entire word's sequence. "CAT" in mirror is not "backward-C backward-A backward-T" in original order; it's "backward-T backward-A backward-C".
- Treating symmetric letters carelessly → Even symmetric letters like A and M need their orientation checked. M is symmetric, but if combined with asymmetric letters, the word's overall mirror or water image changes.
Quick reference
- Mirror image = vertical axis flip → left and right swap; order reverses.
- Water image = horizontal axis flip → top and bottom swap; order stays same.
- Symmetric letters (A, H, I, M, O, T, U, V, W, X, Y) are self-mirror images.
- Clock mirrors: 12:00 – original time = mirror time.
- Double reflection (mirror + water) = 180° rotation of original.
Check yourself: 3 questions
1. What will be the mirror image of the word 'RESULT' when a mirror is placed vertically to the right of the word?
2. The time shown on a clock is 3:40. If you see this clock in a plane mirror placed vertically, what time will the mirror image appear to show? (Assume the clock has numbers 1 to 12 marked normally.)
3. Select the correct mirror image of the given figure (containing the letters 'MNP' arranged horizontally), if the mirror is placed vertically to the right.
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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