Class 9 Mathematics Chapter 11 Symmetry, Reflection and Rotation MCQ with Answers

The CBSE has progressively shifted toward MCQs and objective-type questions in Class 9 and above. Why? Because MCQs test three critical competencies: (1) Conceptual recall — you must know the definition of line symmetry, reflection, and rotational symmetry by heart; (2) Visual-spatial reasoning — geometry MCQs often include diagrams, forcing you to visualize transformations accurately; (3) Elimination skill — in a 4-option MCQ, identifying the correct answer also means spotting trap options designed to catch incomplete understanding. In Chapter 11, the CBSE expects you to distinguish between a figure with line symmetry but no rotational symmetry (e.g., a kite), a figure with both (e.g., a square), and a figure with rotational symmetry only (e.g., a swastika). Traditional long-answer questions cannot assess this precision as efficiently. Furthermore, MCQs reward speed and accuracy — two skills that directly translate to exam performance. By practicing 30 diverse MCQs on symmetry, reflection, and rotation, you develop the mental shortcuts and confidence to solve exam questions in 30–45 seconds per item, leaving you time for longer questions in Section B.

**Q1.** Which of the following letters of the English alphabet has a line of symmetry? (A) P (B) Q (C) A (D) Z **Answer: (C) A** | Reason: The letter A is symmetric about a vertical line through its apex; P, Q, Z have no line symmetry. **Q2.** A vertical line drawn through the centre of a rectangle is a line of symmetry. True or False? (A) True (B) False (C) Cannot determine (D) Only for a square **Answer: (A) True** | Reason: A rectangle has 2 lines of symmetry — one vertical and one horizontal, both passing through the centre. **Q3.** When a point (2, 3) is reflected across the y-axis, its image is: (A) (−2, 3) (B) (2, −3) (C) (−2, −3) (D) (3, 2) **Answer: (A) (−2, 3)** | Reason: Reflection across the y-axis changes the sign of the x-coordinate only. **Q4.** An equilateral triangle has a rotational symmetry of order: (A) 1 (B) 2 (C) 3 (D) 4 **Answer: (C) 3** | Reason: An equilateral triangle looks identical after rotation by 120°, 240°, and 360°, so the order is 3. **Q5.** Which shape has only rotational symmetry and no line symmetry? (A) Square (B) Rectangle (C) Swastika (D) Circle **Answer: (C) Swastika** | Reason: A swastika has rotational symmetry of order 4 (90° rotations) but no straight line of symmetry. **Q6.** A circle has how many lines of symmetry? (A) 1 (B) 2 (C) 4 (D) Infinite **Answer: (D) Infinite** | Reason: Any line passing through the centre of a circle is a line of symmetry. **Q7.** The point (5, 0) reflected across the x-axis becomes: (A) (0, 5) (B) (−5, 0) (C) (5, 0) (D) (0, −5) **Answer: (C) (5, 0)** | Reason: Points on the x-axis remain unchanged under reflection across the x-axis. **Q8.** A regular hexagon has a rotational symmetry of order: (A) 4 (B) 5 (C) 6 (D) 8 **Answer: (C) 6** | Reason: A regular hexagon has rotational symmetry at 60°, 120°, 180°, 240°, 300°, and 360°. **Q9.** Which letter has both line and rotational symmetry? (A) S (B) H (C) N (D) Z **Answer: (B) H** | Reason: H is symmetric about a vertical line and a horizontal line, and also has rotational symmetry of order 2. **Q10.** The order of rotational symmetry of a rhombus is: (A) 1 (B) 2 (C) 3 (D) 4 **Answer: (B) 2** | Reason: A rhombus looks identical when rotated by 180° and 360°, so the order is 2.

**Q11.** A figure has 4 lines of symmetry and a rotational symmetry of order 4. The figure is: (A) Rectangle (B) Square (C) Rhombus (D) Kite **Answer: (B) Square** | Reason: A square has 4 lines of symmetry (2 diagonal + 2 through midpoints of opposite sides) and rotational symmetry of order 4 at 90° intervals. **Q12.** When the point (−3, 4) is reflected across the line y = x, the image is: (A) (4, −3) (B) (−3, −4) (C) (4, 3) (D) (3, 4) **Answer: (A) (4, −3)** | Reason: Reflection across y = x swaps the x and y coordinates: (a, b) → (b, a). **Q13.** A quadrilateral has exactly one line of symmetry. It cannot be a: (A) Kite (B) Isosceles trapezium (C) Rectangle (D) Both (B) and (C) **Answer: (D) Both (B) and (C)** | Reason: A rectangle has 2 lines of symmetry, and an isosceles trapezium has 1; only a kite (non-square) has exactly 1. **Q14.** The point P is reflected across the y-axis to get P′, and then P′ is reflected across the x-axis to get P″. If P = (6, 8), what is P″? (A) (−6, −8) (B) (−6, 8) (C) (6, −8) (D) (−8, −6) **Answer: (A) (−6, −8)** | Reason: P(6, 8) → P′(−6, 8) after y-axis reflection; P′(−6, 8) → P″(−6, −8) after x-axis reflection. **Q15.** A figure rotated by 72° looks identical. The order of rotational symmetry is: (A) 3 (B) 4 (C) 5 (D) 6 **Answer: (C) 5** | Reason: If 360° ÷ 72° = 5, the figure has rotational symmetry of order 5 (a regular pentagon). **Q16.** The letter 'Z' has: (A) One line of symmetry and rotational symmetry of order 2 (B) Two lines of symmetry (C) Rotational symmetry of order 2 only, no line symmetry (D) No symmetry **Answer: (C) Rotational symmetry of order 2 only, no line symmetry** | Reason: Z looks identical when rotated 180° but has no line of symmetry. **Q17.** A kite ABCD has AB = AD and CB = CD. The line of symmetry is: (A) AC (B) BD (C) The perpendicular bisector of AC (D) The perpendicular bisector of BD **Answer: (A) AC** | Reason: In a kite, the diagonal joining the vertices between unequal sides is the line of symmetry. **Q18.** When a triangle is rotated 360°, it looks identical. Its rotational symmetry order is: (A) 0 (B) 1 (C) 3 (if equilateral) (D) Only equilateral triangles have rotational symmetry **Answer: (B) 1** | Reason: Any figure looks identical at 360°, so every figure has rotational symmetry of at least order 1; only equilateral or isosceles triangles have order > 1. **Q19.** A regular polygon has a rotational symmetry of order 8. How many sides does it have? (A) 6 (B) 8 (C) 10 (D) 12 **Answer: (B) 8** | Reason: A regular n-gon has rotational symmetry of order n; so a rotational order of 8 means 8 sides. **Q20.** The point (−4, −7) is reflected across the origin (by a 180° rotation). The image is: (A) (4, 7) (B) (−4, 7) (C) (4, −7) (D) (7, 4) **Answer: (A) (4, 7)** | Reason: Reflection through the origin (or 180° rotation) maps (a, b) to (−a, −b).

**Q21. Assertion (A):** A parallelogram has rotational symmetry of order 2. **Reason (R):** The diagonals of a parallelogram bisect each other at the centre, making 180° rotation identical. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (A) Both A and R are true, and R is the correct explanation of A** | Reason: A parallelogram has rotational symmetry of order 2 because the diagonals intersect at the centre, and 180° rotation maps it onto itself. **Q22. Assertion (A):** The graph of y = x² has a line of symmetry. **Reason (R):** The parabola y = x² is symmetric about the y-axis. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (A) Both A and R are true, and R is the correct explanation of A** | Reason: y = x² is symmetric about the y-axis (the line of symmetry), verified by f(−x) = f(x). **Q23. Assertion (A):** An isosceles trapezium has exactly one line of symmetry. **Reason (R):** An isosceles trapezium has equal legs but non-equal parallel sides. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (B) Both A and R are true, but R is not the correct explanation** | Reason: An isosceles trapezium has one line of symmetry, but this is because of its symmetry about the perpendicular bisector of the parallel sides, not merely because of equal legs. **Q24. Assertion (A):** The letter 'O' has infinite lines of symmetry and rotational symmetry of any order. **Reason (R):** A circle (which resembles 'O') has infinite lines of symmetry and can be rotated by any angle and still look identical. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (A) Both A and R are true, and R is the correct explanation of A** | Reason: A perfect circle has infinite lines of symmetry (all diameters) and infinite-fold rotational symmetry. **Q25. Assertion (A):** When a point P(a, b) is reflected across the line x = k, the image P′ is (2k − a, b). **Reason (R):** The line x = k is a vertical line, so reflection changes only the x-coordinate. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (A) Both A and R are true, and R is the correct explanation of A** | Reason: Reflection across x = k maps (a, b) to (2k − a, b) because the vertical line x = k is the perpendicular bisector of P and P′. **Q26. Assertion (A):** A rhombus with all angles = 90° is a square. **Reason (R):** A square has 4 lines of symmetry, while a non-square rhombus has only 2. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (B) Both A and R are true, but R is not the correct explanation** | Reason: A rhombus with 90° angles is a square (correct), and the difference in line symmetry is an observation, but not the definition of a square. **Q27. Assertion (A):** A figure with rotational symmetry of order n always has n lines of symmetry. **Reason (R):** The star (★) has rotational symmetry of order 5 but only 5 lines of symmetry. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (D) A is false, but R is true** | Reason: A is false; many figures have rotational symmetry without matching line symmetry (e.g., a swastika has order 4 rotation but 0 lines of symmetry). The example of a star supports this. **Q28. Assertion (A):** The reflection of the point (a, −b) across the line y = −x is (b, −a). **Reason (R):** Reflection across y = −x swaps coordinates and negates one of them: (a, b) → (−b, −a). (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (A) Both A and R are true, and R is the correct explanation of A** | Reason: (a, −b) → (b, −a) under reflection across y = −x, and the formula in R correctly describes the transformation. **Q29. Assertion (A):** A rectangle has a rotational symmetry of order 2 and 2 lines of symmetry. **Reason (R):** The diagonals of a rectangle bisect each other but are not perpendicular. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (B) Both A and R are true, but R is not the correct explanation** | Reason: A rectangle has order-2 rotational symmetry and 2 lines of symmetry (both true), but this is not explained by the diagonals; rather, by the congruence of opposite sides. **Q30. Assertion (A):** If a figure has a rotational symmetry of order 3, then rotating it by 120° returns it to its original position. **Reason (R):** Rotational symmetry of order n means the figure is identical after rotation by 360°/n. (A) Both A and R are true, and R is the correct explanation of A (B) Both A and R are true, but R is not the correct explanation (C) A is true, but R is false (D) A is false, but R is true **Answer: (A) Both A and R are true, and R is the correct explanation of A** | Reason: Order 3 = 360° ÷ 3 = 120° rotation, confirming both statements and their logical link.

CBSE examiners design plausible wrong answers to exploit three common misconceptions: **Trap 1: Confusing Line Symmetry with Rotational Symmetry.** A figure with one line of symmetry (e.g., a kite) may have no rotational symmetry. Students often tick an option saying "it has symmetry, so both types must apply." Always check each type independently. Example: An isosceles triangle has 1 line of symmetry but no rotational symmetry; the trap option might say "rotational order 1," which is technically true for all figures but misleading. **Trap 2: Miscounting Lines of Symmetry.** A square has 4 lines of symmetry (2 diagonal + 2 perpendicular bisectors of opposite sides). A rectangle has only 2. Students who mentally "rotate" shapes often overcount. Always draw or visualize the line and check if the left and right (or top and bottom) halves mirror perfectly. **Trap 3: Assuming All Polygons with n Sides Have Order-n Rotational Symmetry.** Only *regular* polygons have rotational symmetry of order n. An irregular hexagon does not. The trap option uses a property of regularity without stating it explicitly. **Trap 4: Reflection Coordinate Mistakes.** Students often swap x and y, forget the sign change, or apply the wrong reflection axis. Example: Reflecting (3, 5) across the y-axis gives (−3, 5), not (3, −5). Write out the reflection rule before answering: y-axis reflection → (−x, y); x-axis reflection → (x, −y); y = x reflection → (y, x); origin reflection → (−x, −y). **Trap 5: Thinking "Order 1" Means "No Symmetry."** Every figure has rotational symmetry of order 1 (360° rotation). But in CBSE language, a figure with "only order 1" is often called having "no rotational symmetry." Read the question carefully: does it ask for the order, or does it ask if rotational symmetry exists? **Trap 6: Letters and Symmetry.** The letter 'S' is a classic trap. Students think it might have rotational symmetry of order 2 (180° turn looks like an 'S'), but actually, a rotated 'S' looks backwards, not identical. Similarly, 'N' and 'Z' have order-2 rotational symmetry but zero lines of symmetry — yet students confuse this with 'S.' Start a 3-day free trial at cbsetutor.ai to access interactive symmetry diagrams, instant feedback on your answers, and personalized hints to overcome these traps.

In a typical CBSE Class 9 Mathematics exam, you face 6–8 MCQs per chapter in Section A (1 mark each). Chapter 11 (Symmetry) usually allocates 5–7 minutes to MCQs. Here's a battle-tested strategy: **Step 1: Read & Categorize (30 seconds per MCQ).** Read the question and all four options. Mentally tag the question: "Definition," "Diagram," "Coordinate," or "Assertion-Reason." This prevents you from overthinking. **Step 2: Eliminate Obvious Traps (15 seconds).** Cross out 1–2 obviously wrong options. In Chapter 11, if an option contradicts the definition of rotational symmetry or makes a coordinate error, eliminate it immediately. **Step 3: Solve or Visualize (30 seconds).** For definition-based MCQs, recall the fact. For diagram-based questions, visualize the reflection or rotation in your mind or lightly sketch on the question paper. For coordinates, apply the reflection rule formula (see Trap 2 above). For assertion-reason, evaluate both independently. **Step 4: Verify Against Distractors (15 seconds).** Before marking, reread the correct option and ask: "Does this exactly match the question asked?" Trap options often include correct statements that don't answer the question (e.g., a true statement about diagonals that doesn't explain a given symmetry property). **Time Targets:** - Easy MCQs (Q1–Q10): 40 seconds each. You should finish all 10 in ≈7 minutes and earn full marks (10/10). - Medium MCQs (Q11–Q20): 50–60 seconds each. Aim for 8/10 in 9–10 minutes. - Hard Assertion-Reason (Q21–Q30): 60–90 seconds each. Aim for 6/10 in 9–12 minutes. **If You Get Stuck:** Mark a question "to revisit" in 10 seconds flat. Return to it after completing all straightforward MCQs. Spend no more than 2 minutes on any single MCQ in a timed exam; guessing with logic beats blank submissions. **Final Check (2 minutes):** If time allows, verify your answers for assertion-reason MCQs. These are highest-value because one logical slip (e.g., choosing (B) when (A) is correct) costs a full mark.

Chapter 11 tests your spatial intuition as much as your conceptual knowledge. The 30 MCQs in this guide span all difficulty levels and question types in the 2024-25 CBSE pattern. By practicing these, you'll: 1. **Memorize** the definition, properties, and formulas for line symmetry, reflection, and rotational symmetry. 2. **Visualize** geometric transformations without error — a critical skill for Class 9 and beyond. 3. **Avoid** common traps that cost marks in real exams. 4. **Manage time** efficiently in a high-pressure exam environment. The NCERT Chapter 11 content is compact, but examiners test it deeply through MCQs that require precision. A single misunderstanding — say, confusing "rotational symmetry of order 1" with "no rotational symmetry" — can result in systematic errors across multiple questions. That's why assertion-reason MCQs (Q21–Q30) are so valuable: they force you to articulate *why* a statement is true, not just *that* it is true. This depth of understanding translates to higher scores on problem-solving questions in Sections B and C. After completing all 30 MCQs here, move to NCERT worked examples and construct your own diagrams to reinforce visual learning. With this balanced approach — MCQ precision + NCERT conceptual depth — you'll secure 95%+ on Chapter 11 in your unit or board exam.