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SBI PO Direction & Distance

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This page covers SBI PO Direction & Distance with complete concept notes, 6 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Direction & Distance— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

You start from a point, follow given directions (North, South, East, West), and determine the final position or shortest distance back to start. The key is visualizing the path and using coordinate geometry or Pythagoras theorem

Key Rules

North is positive Y-axis, East is positive X-axis, South is negative Y-axis, West is negative X-axis. Always draw a rough diagram. Right turn means clockwise rotation (N→E→S→W). Left turn means anticlockwise rotation (N→W→S→E).

Formula BlockMemorise — at least one formula appears in every paper
Shortest Distance = √[(x2-x1)² + (y2-y1)²]
Displacement = Final position - Initial position
Right turn sequence: N→E→S→W→N (clockwise)
Left turn sequence: N→W→S→E→N (anticlockwise)
Exam PatternsWhat examiners ask — read before attempting PYQs

SSC asks three main types - (1) Find final position after multiple movements (2) Calculate shortest distance between start and end points (3) Determine direction of final position from starting point. Questions often include multiple turns to confuse students.

ShortcutsUse these to save 30–60 seconds per question

Use coordinate method. Place starting point at origin (0,0). Move North = +Y, South = -Y, East = +X, West = -X.

Plot final coordinates and apply distance formula. This eliminates drawing errors.

Worked ExampleSolve this step-by-step before moving on

Ram starts from home, walks 4km North, then 3km East, then 2km South. Find shortest distance to reach home. Solution: Place home at (0,0). After 4km North: (0,4).

After 3km East: (3,4). After 2km South: (3,2). Final position = (3,2).

Shortest distance = √[(3-0)² + (2-0)²] = √[9+4] = √13 = 3.6km Worked Example 2: Sita walks 5km East, turns right, walks 12km, turns right again, walks 5km. How far is she from start? Solution: Start at (0,0). 5km East: (5,0). Turn right (now facing South), walk 12km: (5,-12).

Turn right again (now facing West), walk 5km: (0,-12). Distance from start = √[(0-0)² + (-12-0)²] = 12km Advanced Shortcut: For rectangular paths, if you return to same X or Y coordinate, the distance equals the remaining coordinate value. In example 2, X-coordinate returned to 0, so distance = Y-coordinate = 12km. Direction Shortcut: Final direction from start can be found using coordinates.

If final position is (a,b), then direction is determined by signs: (+,+) = Northeast, (+,-) = Southeast, (-,+) = Northwest, (-,-) = Southwest.

Exam TrapsCommon mistakes students make — avoid these

Students confuse left/right turns with compass directions. Remember that turns are relative to current facing direction, not absolute directions. If facing North and turn right, you face East.

If facing East and turn right, you face South. Always track current facing direction after each turn. Another major error is calculation mistakes in distance formula. Students forget to square the terms or make errors in square root calculation.

Practice mental calculation of common squares: 3²=9, 4²=16, 5²=25, 12²=144, 13²=169. Time-saving tip: Recognize special triangles. 3-4-5 triangle has hypotenuse 5. 5-12-13 triangle has hypotenuse 13. 8-15-17 triangle has hypotenuse 17. If coordinates match these patterns, you can instantly write the answer without calculation.

Key Points to Remember

  • Always place starting point at origin (0,0) for coordinate method
  • North = +Y axis, South = -Y axis, East = +X axis, West = -X axis
  • Distance formula: √[(x2-x1)² + (y2-y1)²]
  • Right turn sequence: N→E→S→W (clockwise rotation)
  • Left turn sequence: N→W→S→E (anticlockwise rotation)
  • Draw rough diagram to visualize the path before calculating
  • For rectangular paths returning to same coordinate, distance equals remaining coordinate
  • Track current facing direction after every turn to avoid confusion
  • Memorize special triangles: 3-4-5, 5-12-13, 8-15-17 for quick calculation
  • Final direction from start depends on coordinate signs: (+,+)=NE, (+,-)=SE, (-,+)=NW, (-,-)=SW

Exam-Specific Tips

  • Pythagoras theorem: c² = a² + b² where c is hypotenuse
  • 3-4-5 triangle: sides 3, 4 give hypotenuse 5
  • 5-12-13 triangle: sides 5, 12 give hypotenuse 13
  • 8-15-17 triangle: sides 8, 15 give hypotenuse 17
  • √2 = 1.414 (for 45-degree movements)
  • √3 = 1.732 (for 60-degree movements)
  • Right angle = 90 degrees rotation
  • Straight angle = 180 degrees rotation
Practice MCQs

Direction & Distance — Practice Questions

6graded MCQs · easy to hard · full solution & trap analysis

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Practice 1easy

Rajesh starts from his home facing North. He walks 8 km straight, then turns right and walks 6 km. After that, he turns left and walks 4 km. Finally, he turns right and walks 5 km. In which direction is Rajesh now facing, and how far is he from his starting point in the East-West direction?

Practice 2easy

Priya starts at a point facing South. She walks 10 km forward, turns left and walks 7 km, then turns right and walks 3 km. What is her final position relative to her starting point?

Practice 3easy

Arun walks 12 km North from point A, then turns right and walks 9 km. He then turns left and walks 5 km. How far is Arun from point A in the East direction?

Practice 4easy

Neha starts from her office facing West. She walks 20 km forward, then turns right and walks 12 km. After that, she turns left and walks 8 km. What is her displacement from the office in the North-South direction?

Practice 5medium

Rajesh starts from point A facing North. He walks 8 km, then turns right and walks 6 km. After that, he turns left and walks 4 km. Finally, he turns right and walks 3 km to reach point B. In which direction is point B with respect to point A, and what is the straight-line distance between them?

Practice 6hard

Rajesh starts from point A facing North. He walks 8 km, then turns 45° to his right (Northeast direction) and walks 6 km. From there, he turns left and walks 5 km North. Finally, he turns 90° to his left and walks 4 km West. What is Rajesh's final direction from point A, and approximately how far is he from point A?

60-Second Revision — Direction & Distance

  • Remember: Use coordinate method with start point at (0,0)
  • Formula: Distance = √[(x2-x1)² + (y2-y1)²]
  • Trap: Track facing direction after each turn, not absolute directions
  • Shortcut: Recognize 3-4-5, 5-12-13, 8-15-17 triangles for instant answers
  • Technique: Right turns go N→E→S→W, left turns go N→W→S→E
  • Quick check: For rectangular paths, final distance often equals one coordinate value
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