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Starting–Ending Position

Introduction

The Starting-Ending Position pattern asks learners to find where a person ends up relative to their starting point after one or more movements. This pattern is important because it combines direction sense with basic displacement - a frequent topic in competitive aptitude tests.

Mastering this helps in solving displacement, shortest-distance, and relative-position questions quickly and accurately.

Pattern: Starting–Ending Position

Pattern

Key concept: Treat each movement as a vector (direction + magnitude). Sum horizontal (E/W) and vertical (N/S) components to get net displacement and direction.

- Convert each step into north/south and east/west components.
- Net north-south = (north total) - (south total). Net east-west = (east total) - (west total).
- Distance from start = √(net NS² + net EW²). Direction from start given by the sign and combination of net components (e.g., net north & net east = North-East).

Step-by-Step Example

Question

A starts from point O, walks 3 m North, then 4 m East, and then 3 m South. How far and in which direction is A from O?

Solution

  1. Step 1: Identify and list movements

    Movements: 3 m North, 4 m East, 3 m South.

  2. Step 2: Compute net north-south component

    North total = 3 m; South total = 3 m → Net NS = 3 - 3 = 0 m.

  3. Step 3: Compute net east-west component

    East total = 4 m; West total = 0 m → Net EW = 4 - 0 = 4 m (East).

  4. Step 4: Compute straight-line distance

    Distance = √(Net NS² + Net EW²) = √(0² + 4²) = 4 m.

  5. Step 5: Determine direction from start

    Net components → 0 m North/South and 4 m East → Direction = East.

  6. Final Answer:

    4 m East → Option A

  7. Quick Check:

    Combine movements: North 3 and South 3 cancel → only 4 m East remains. Distance 4 m East ✅

Quick Variations

1. Movements with unequal NS components (use Pythagoras to get diagonal displacement).

2. Problems where all movements are along a straight line (net is simple subtraction).

3. Include diagonal steps (e.g., North-East) - break them into components if magnitudes allow.

4. Ask for direction only, distance only, or both.

Trick to Always Use

  • Step 1: Convert each move into N/S and E/W totals (positive for North/East, negative for South/West).
  • Step 2: Sum NS and EW separately to get net components.
  • Step 3: Use √(NS²+EW²) for distance and combine signs for direction (e.g., +NS & +EW = North-East).

Summary

Summary

  • Compute net north-south and east-west components separately to find relative position.
  • Use Pythagoras to calculate straight-line distance from start to end.
  • Direction is given by the signs of net components (use NE/SE/NW/SW for diagonals).
  • Quick cancellation (equal opposite movements) simplifies many problems - check for it first.

Example to remember:
If movements are 5 m North, 5 m East, 5 m South → net = 5 m East (distance 5 m East).

Practice

(1/5)
1. A person walks 4 m North, then 3 m East, and finally 4 m South. How far and in which direction is he from the starting point?
easy
A. 3 m East
B. 4 m West
C. 5 m East
D. 7 m North

Solution

  1. Step 1: List the movements

    North = 4 m, East = 3 m, South = 4 m.

  2. Step 2: Find net North-South

    4 - 4 = 0 m → cancels out.

  3. Step 3: Find net East-West

    3 - 0 = 3 m East.

  4. Step 4: Compute final displacement

    Only 3 m East remains → distance = 3 m, direction = East.

  5. Final Answer:

    3 m East → Option A

  6. Quick Check:

    Equal North-South cancels; only East movement left ✅
Hint: Cancel opposite directions first before calculating net displacement.
Common Mistakes: Adding distances instead of cancelling opposite directions.
2. A boy walks 6 m South, then 8 m East, and finally 6 m North. Find his distance and direction from the starting point.
easy
A. 8 m East
B. 6 m North-East
C. 10 m South
D. 8 m West

Solution

  1. Step 1: Identify movements

    South = 6 m, East = 8 m, North = 6 m.

  2. Step 2: Compute net North-South

    6 South and 6 North cancel → 0 m.

  3. Step 3: Compute net East-West

    8 m East → final displacement 8 m East.

  4. Final Answer:

    8 m East → Option A

  5. Quick Check:

    Vertical movement cancels; only East remains ✅
Hint: Opposite vertical moves often cancel each other; only the horizontal remains.
Common Mistakes: Forgetting to cancel opposite movements.
3. A person walks 5 m North, 12 m East, and 5 m South. How far is he from the starting point?
easy
A. 12 m
B. 10 m
C. 15 m
D. 5 m

Solution

  1. Step 1: Note movements

    North = 5 m, East = 12 m, South = 5 m.

  2. Step 2: Calculate net NS

    5 - 5 = 0 m.

  3. Step 3: Calculate net EW

    12 - 0 = 12 m East.

  4. Step 4: Compute displacement

    √(0² + 12²) = 12 m.

  5. Final Answer:

    12 m → Option A

  6. Quick Check:

    Only East movement remains after vertical cancellation ✅
Hint: When opposite sides equal, displacement = remaining single direction distance.
Common Mistakes: Using wrong direction for final displacement.
4. A man walks 6 m North, 8 m East, and then 6 m South. How far and in which direction is he from his starting point?
medium
A. 8 m East
B. 6 m North-East
C. 10 m East
D. 8 m West

Solution

  1. Step 1: Record all movements

    North = 6 m, East = 8 m, South = 6 m.

  2. Step 2: Find net vertical movement

    6 - 6 = 0 m.

  3. Step 3: Find net horizontal movement

    8 m East → remains unchanged.

  4. Step 4: Displacement

    √(0² + 8²) = 8 m East.

  5. Final Answer:

    8 m East → Option A

  6. Quick Check:

    Up and down cancel, only rightward (East) 8 m remains ✅
Hint: When equal North and South distances appear, result lies directly East or West.
Common Mistakes: Calculating unnecessary diagonal when vertical cancels.
5. A person walks 5 m North, 5 m East, and then 5 m South. What is the distance and direction from his starting point?
medium
A. 5√2 m North-East
B. 5 m East
C. 10 m East
D. 7 m South

Solution

  1. Step 1: Identify movements

    North = 5 m, East = 5 m, South = 5 m.

  2. Step 2: Calculate net NS

    5 - 5 = 0 → cancels.

  3. Step 3: Calculate net EW

    5 - 0 = 5 → East.

  4. Step 4: Compute displacement

    √(0² + 5²) = 5 m East.

  5. Final Answer:

    5 m East → Option B

  6. Quick Check:

    Vertical movement cancels → displacement purely East ✅
Hint: Subtract opposite movements before applying distance formula.
Common Mistakes: Using diagonal formula unnecessarily.

Mock Test

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