Direction Sense – Study Notes (Himachal Pradesh TET – Reasoning Ability)
1. Simple Explanation
Direction sense problems are a type of spatial reasoning question in which you are asked to determine the relative position of one object or person with respect to another after a series of movements.
Typical directions used are North (N), South (S), East (E), West (W), and sometimes NE, NW, SE, SW.
Key idea:
Treat the movement as a change in coordinates on a 2‑D plane.
- N → +y
- S → –y
- E → +x
- W → –x
After all moves, compute the final coordinates of each person/object. The direction from one point to another is then derived by comparing the coordinate differences.
2. Key Points to Remember
| # | Concept | Why It Matters | Quick Tip |
|---|---|---|---|
| 1 | Start position | All relative positions are measured from a common origin (often “here” or “0,0”). | Assume the starting location as (0,0). |
| 2 | Move vectors | Each direction contributes a vector (Δx, Δy). | Write a small table: N:(0,1), S:(0,-1), E:(1,0), W:(-1,0). |
| 3 | Cumulative displacement | Add vectors step‑by‑step to find final coordinates. | Keep a running sum; use a sheet if many steps. |
| 4 | Relative direction | Compare final coordinates of two points. | Use the sign of Δx and Δy: • Δx>0, Δy>0 → NE • Δx>0, Δy=0 → E • Δx=0, Δy<0 → S … |
| 5 | Opposite direction | “Opposite” means 180° apart. | If A is E of B, B is W of A. |
| 6 | Left/Right | Determined by the person’s own orientation, not absolute. | If a person faces N, then E is to his right. |
| 7 | Multiple people | Keep separate coordinates for each person. | Label them (A, B, C…) and update independently. |
| 8 | Clock‑wise vs. Anti‑clockwise | Useful when directions are given relative to a starting point. | Remember that right turn = +90°; left turn = –90°. |
| 9 | Quick mental checks | Look for cancellations (e.g., N and S cancel). | Simplify before calculating exact coordinates. |
| 10 | Common traps | Misinterpreting “to the right of” vs. “to the left of” when the observer’s orientation changes. | Always ask: “Which way is me facing?” |
3. Worked Example
Question:
In a 2‑D grid, Person A starts at a point and moves as follows:
- N 3 units
- E 2 units
- S 1 unit
- W 4 units
Person B moves:- S 2 units
- E 3 units
- N 4 units
After the moves, where is A relative to B? (Answer in one of the 8 directions.)
Step‑by‑Step Solution
| Person | Step | Direction | Δx | Δy | Cumulative (x, y) |
|---|---|---|---|---|---|
| A | 1 | N | 0 | +3 | (0, 3) |
| A | 2 | E | +2 | 0 | (2, 3) |
| A | 3 | S | 0 | –1 | (2, 2) |
| A | 4 | W | –4 | 0 | (-2, 2) |
| B | 1 | S | 0 | –2 | (0, –2) |
| B | 2 | E | +3 | 0 | (3, –2) |
| B | 3 | N | 0 | +4 | (3, 2) |
Relative vector from B to A
Δx = Ax – Bx = –2 – 3 = –5
Δy = Ay – By = 2 – 2 = 0
So A is 5 units to the West of B.
Answer: West (or W).
Quick Check
- Δx negative → A is left of B → West.
- Δy zero → same horizontal line.
✓ Result matches calculations.
4. Quick Revision Summary
| Topic | What to Do | Quick Hint |
|---|---|---|
| Set origin | Assume start at (0,0). | “Here” = (0,0) |
| Translate moves | Map N=+y, S=–y, E=+x, W=–x. | Write a small key. |
| Accumulate | Add Δx, Δy for each step. | Keep a running total. |
| Compare two points | Δx = x₂–x₁, Δy = y₂–y₁. | Sign of Δx/Δy → direction. |
| Check for cancellations | Cancel opposite moves early. | Simplify before final calc. |
| Remember left/right | Depends on observer’s facing direction. | “Right turn = +90°”. |
| Answer format | One of 8 compass points. | N, S, E, W, NE, NW, SE, SW. |
| Common pitfalls | Misreading “to the right of” when the observer turns. | Clarify observer’s orientation first. |
Final Tips for TET
- Practice with diagrams – draw a simple grid; mark the start and moves.
- Time management – most direction sense questions are solvable in 30‑45 seconds.
- Use shorthand – write MOVES as (Δx,Δy) and add quickly.
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