Direction and Mirror Images – Concepts for Aptitude

Directions and Mirror Images questions test spatial awareness, the ability to interpret reflections, and reasoning skills related to orientation and visualization. Let’s explore each of these topics in detail with techniques, examples, and tips.

1. Directions

Direction-based questions are common in reasoning tests, often involving navigation (north, south, east, west) and distance calculations. Candidates are typically asked to determine the final direction or distance after a series of turns and movements.

Key Directions Concepts

  1. Cardinal Directions:
    • The main directions are North (N), South (S), East (E), and West (W).
    • Intermediate directions include Northeast (NE), Northwest (NW), Southeast (SE), and Southwest (SW).
  2. Turns:
    • Right Turn: A 90° clockwise turn from the current direction.
    • Left Turn: A 90° counterclockwise turn from the current direction.
    • U-turn: A 180° turn, reversing the direction.
  3. Relative Direction:
    • If facing a certain direction, a left turn moves 90° counterclockwise, and a right turn moves 90° clockwise.
    • Example: If facing North, a left turn means facing West, and a right turn means facing East.
  4. Distance Calculation:
    • For questions involving distances, use Pythagoras’ theorem for calculating shortest distances (especially if movements form a right-angled triangle).

Types of Directions Questions

Example 1: Sequence of Directions

Question: A person starts facing North, then turns right, walks 5 km, turns left, walks 10 km, and turns left again to walk 5 km. What direction is the person now facing?

Solution:

  1. Start with North.
  2. Right turn: North → East; walk 5 km.
  3. Left turn: East → North; walk 10 km.
  4. Left turn: North → West; walk 5 km.

Answer: The person is facing West.

Example 2: Distance and Final Position

Question: A man walks 10 km South, then 5 km East, and finally 10 km North. How far is he from his starting point, and in what direction?

Solution:

  1. Draw a rough diagram or visualize the movements:
    • 10 km South.
    • 5 km East.
    • 10 km North (brings him back to the same latitude as the starting point).
  2. Now he is 5 km East of his starting point.

Answer: The man is 5 km East from his starting point.

Tips for Direction Problems

  1. Draw a Diagram: Visual aids help prevent confusion, especially for complex sequences.
  2. Mark Turns Step-by-Step: Track each direction after every turn.
  3. Identify Right Triangles: For shortest distances, use Pythagoras’ theorem when appropriate.

2. Mirror Images

Mirror image questions test the ability to visualize how an object, number, letter, or shape appears in a mirror reflection. These questions are commonly seen in verbal reasoning tests and involve spatial visualization skills.

Key Mirror Image Concepts

  1. Lateral Inversion:
    • A mirror placed vertically (to the left or right) will create a left-to-right inversion.
    • This means the left side of the object becomes the right in the mirror image, and vice versa.
  2. Horizontal Inversion:
    • When a mirror is placed horizontally (below or above), it creates a top-to-bottom inversion.
    • The top of the object appears at the bottom in the mirror image, and the bottom appears at the top.
  3. Mirror Images of Letters and Numbers:
    • Letters and numbers can appear reversed in a mirror. Some, like A, H, I, M, O, T, U, V, W, X, Y, are symmetrical, meaning they look the same in a mirror.
    • Other letters and numbers (e.g., E, 3, 2, 4) will have distinct left-to-right reversals.

Types of Mirror Image Questions

Example 1: Finding the Mirror Image of a Word

Question: Find the mirror image of the word “OAT” if the mirror is placed vertically to the right.

Solution:

  1. Draw the letters in reverse order:
    • “OAT” in a mirror would appear as “TAO” from left to right.
  2. Consider each letter’s shape and orientation.
    • Since the mirror is on the right, “OAT” becomes “TAO” as a mirror image.

Answer: The mirror image is TAO

Example 2: Mirror Image of a Number

Question: What is the mirror image of the number 8084 if the mirror is placed vertically to the right?

Solution:

  1. Reverse the order of the digits: “808” becomes “808.”
  2. Check the lateral inversion of each digit:
    • 8, 0, and 8 are reversed as they appear in a mirror on the right.

Answer: The mirror image is 808.

Example 3: Clock Reflection in a Mirror

Question: A clock shows 3:15. What time will it show in a mirror?

Solution:

  1. In a mirror, clock reflections are reversed by 12 hours (convert to 12-hour clock format).
  2. Subtract the given time from 11:60:
    • Mirror time = 11:60 – 3:15 = 8:45.

Answer: The mirror reflection shows 8:45.

Tips for Mirror Image Problems

  1. Practice Left-to-Right Reversals: Practice with letters, numbers, and common shapes to become familiar with mirror reversals.
  2. Understand Symmetrical Characters: Memorize which letters and numbers are symmetrical (no change in their appearance).
  3. Convert Clock Reflections: For clocks, subtract the time from 11:60 for quick mirroring.

Practice Questions

  1. Direction Practice: A person is facing East, turns left, walks 10 km, then turns right, walks 5 km, and turns left again to walk 10 km. What direction is the person now facing?
  2. Mirror Image Word: What is the mirror image of the word “AOI” if the mirror is on the right?
  3. Clock Mirror Image: A clock shows 9:20. What time will it show in a mirror reflection?

Solutions to Practice Questions

  1. Answer: The person is facing North.
  2. Answer: The mirror image of “AOI” would be IOA.
  3. Answer: The mirror time for 9:20 is 2:40.

An alphanumeric series is a common topic in aptitude tests, especially in the reasoning section. This topic tests a student’s ability to identify patterns and relationships in sequences of letters, numbers, or a combination of both. It involves recognizing order, skipping certain characters, and understanding the logic behind each progression in the series.

Read concepts and formulas for: Statement & Conclusion

Refer Aptitude Questions with Solutions on Direction Sense and Mirror Images: https://www.learntheta.com/aptitude-questions-direction-sense/

Practice Aptitude Questions on Direction Sense and Mirror Images with LearnTheta’s AI Practice Platform: https://www.learntheta.com/placement-aptitude/

Practice
Scroll to Top