Direction Sense – Reasoning Ability
For Andhra Pradesh Police Constable (APPC) Examination
1. Simple Explanation
Direction sense tests your ability to understand and reason about spatial relationships—where things are located relative to one another, how they move, and how distances change when directions change.
Typical problems ask you to:
- Identify the position of a point after a series of turns or moves.
- Determine the direction from one point to another.
- Work out distances or times when directions change.
Think of it as a mini‑navigation test: you must “walk” through the scenario in your mind (or with a sketch) and keep track of every turn and move.
2. Key Points
| Concept | What to Look For | Quick Tip |
|---|---|---|
| Compass Directions | N, S, E, W, NE, SE, SW, NW | Remember the mnemonic NESW (North‑East‑South‑West). |
| Relative Directions | Ahead, Behind, Left, Right, Opposite | Use a simple 2‑D coordinate system; left = negative X, right = positive X. |
| Turns | 90°, 180°, 270°, or “left/right” | 90° left = counter‑clockwise; 90° right = clockwise. |
| Distance & Time | “Walks 5 km at 5 km/h” → 1 h | Use Distance = Speed × Time; keep units consistent. |
| Multiple Moves | Sequence of moves → final position | Draw a step‑by‑step diagram or use vector addition. |
| Symmetry & Reflection | Mirror image across a line | Often the answer is “opposite direction” or “same distance”. |
| Circular Motion | “Completes a circle” → back to start | 360° turn = return to original direction. |
| Coordinate Axes | X‑axis = East/West, Y‑axis = North/South | Positive X = East, Negative X = West; Positive Y = North, Negative Y = South. |
| Angles | 45°, 30°, 60° etc. | 45° = NE, 135° = SE, 225° = SW, 315° = NW. |
| Relative Speed | Two people moving towards each other | Use Relative Speed = Sum of speeds to find meeting point. |
3. Worked Example
Problem
**A person starts at point A. He moves 4 km north. Then he turns 90° right and walks 3 km. After that he turns 45° left and walks 2 km. Finally, he turns 90° right and walks 1 km.
Find the direction of the final point (from the starting point A).
Solution
-
Set up a coordinate system
- X‑axis: East (positive), West (negative).
- Y‑axis: North (positive), South (negative).
-
Track each segment
| Step | Direction | Distance | ΔX | ΔY |
|---|---|---|---|---|
| 1 | North | 4 km | 0 | +4 |
| 2 | 90° right (East) | 3 km | +3 | 0 |
| 3 | 45° left from East → North‑East | 2 km | +√2 ≈ +1.414 | +√2 ≈ +1.414 |
| 4 | 90° right from North‑East → South‑East | 1 km | +1 | –1 |
- Sum the deltas
| ΔX | ΔY |
|---|---|
| 0 + 3 + 1.414 + 1 = 5.414 km | 4 + 0 + 1.414 – 1 = 4.414 km |
-
Determine the final bearing
- The final point is 5.414 km east and 4.414 km north of A.
- Angle from north:
[ \theta = \tan^{-1}!\Big(\frac{5.414}{4.414}\Big) \approx \tan^{-1}(1.225) \approx 50^\circ ] - So the direction is about 50° east of north (or North‑East but a little more eastward).
-
Answer
The final point lies NE of A, roughly 50° east of north.
4. Quick Revision Summary
| Topic | What to Remember |
|---|---|
| Compass | N, NE, E, SE, S, SW, W, NW |
| 90° Turns | Right = clockwise, Left = counter‑clockwise |
| Relative Positions | Ahead = +Y, Behind = –Y; Left = –X, Right = +X |
| Distance Calculation | Distance = Speed × Time; keep units |
| Vector Addition | Sum ΔX and ΔY for each step |
| Angle Conversion | 45° = NE, 135° = SE, 225° = SW, 315° = NW |
| Circular Motion | 360° turn brings you back to start |
| Common Tricks | Use simple sketches; label each move; check units |
Tips for Exam Day
- Always draw a quick sketch – even a crude diagram clears confusion.
- Label axes; use +X = East, +Y = North.
- Work step‑by‑step; don’t try to solve in your head.