Direction and Distance
About 7 min · General Intelligence and Reasoning · English
Time worked out from the lesson's 540 words at 150 words a minute, plus a minute for each question.
Direction and Distance questions test your ability to track movement on a compass and calculate the shortest distance or final position of a person relative to the starting point. These problems appear simple but require careful attention to directions (North, South, East, West) and basic geometry for distance calculations.
Key ideas
- Cardinal directions: North (N), South (S), East (E), West (W) are the four main compass points. North is always at the top of your mental map, South at bottom, East to the right, West to the left.
- Turns and rotations: A right turn from North leads to East; a left turn from North leads to West. After any turn, your new facing direction becomes the reference for the next instruction.
- Opposite directions: North ↔ South are opposites; East ↔ West are opposites. Moving North then South by the same distance brings you back to the starting latitude.
- Net displacement: If someone moves North 5 km then South 3 km, the net northward displacement is 5 − 3 = 2 km. Similarly, East and West movements cancel partially.
- Pythagorean theorem for distance: When final position involves both North–South and East–West displacement, the straight-line distance is √(NS² + EW²), where NS is net North–South distance and EW is net East–West distance.
Watch out for
- Confusing left and right turns: After facing North, a right turn leads to East, not West. Draw a compass rose on your paper and physically trace the turn to confirm. Wrong turn direction cascades through the entire problem.
- Adding all distances instead of using net displacement: A student walks 5 km North and 3 km South, then calculates total as 8 km. Correct approach: net displacement is 5 − 3 = 2 km North. Always calculate net North–South and East–West separately before applying Pythagorean theorem.
- Forgetting to apply Pythagorean theorem: When both North–South and East–West displacements exist, the straight-line distance is NOT the sum of the two. You must use √(NS² + EW²). Simple addition gives the wrong answer.
Quick reference
- Pythagorean distance: √(horizontal² + vertical²) for final straight-line distance from start.
- Net displacement = forward − backward in each axis before calculating distance.
- Right turn cycle: N → E → S → W → N (clockwise). Left turn reverses it.
- Common triplets: (3,4,5), (5,12,13), (8,15,17) — memorize these to save time.
- Always sketch: A quick compass cross (N-S-E-W) helps prevent directional errors.
Check yourself: 3 questions
1. A man walks 5 km towards North, then turns right and walks 3 km, then turns right again and walks 5 km. In which direction is he now from his starting point?
2. Ravi starts from his home and walks 40 m towards South. He then turns left and walks 30 m, then turns left again and walks 40 m. Finally, he turns right and walks 20 m. How far is he from his home?
3. A boy walks 15 m towards West from point A to point B. He then turns right and walks 20 m to point C, then turns right again and walks 28 m to point D. Finally, he turns right and walks 20 m to point E. What is the shortest distance between point A and point E?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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