Direction & Distance Guide & Practice
Practice displacement, shadow-based direction, multi-step journeys, and two-person movement problems with shortcuts and free mock tests. Explore dynamic solver blueprints, master fundamental equations, examine step-by-step solved examples, and practice with real exam-grade mock test sets.
1. Fundamentals & Definitions
- Direction: The position of one thing with respect to another or a reference point.
- Distance: The measurement of the shortest distance (displacement) between two points.
- Starting Point (Origin): The point where the movement begins.
- Destination: The point where the movement ends.
- Main Directions: There are four main directions: North, South, East, and West.
- Sub-Directions: There are four sub-directions (also called cardinal directions): North-East (N-E), North-West (N-W), South-East (S-E), and South-West (S-W).
- Turns:
- Right Turn: Always a clockwise (CW) turn.
- Left Turn: Always an anticlockwise (ACW) turn.
| Direction | Opposite Direction |
|---|---|
| North | South |
| East | West |
2. Core Concepts & Formulas
Types of Direction Problems
- Turns and Rotations: A person or object makes a series of left/right turns (or clockwise/anticlockwise rotations by a specific degree). The final direction or position is asked.
- Distance and Displacement: Displacement is the shortest distance between the initial and final points. This is different from the total distance traveled. If a person returns to the starting point, their displacement is zero.
- Shadow-Based Problems: These questions rely on the position of the sun.
- From sunrise until just before noon (12 PM), a shadow is cast to the West.
- From just after noon (12 PM) until sunset, a shadow is cast to the East.
- At exactly 12 PM (noon), there is no shadow.
- A shadow is always cast on the opposite side of the sun.
- Coded Directions: Directions and distances are represented by symbols. You must decode the symbols to solve the puzzle.
Finding the Shortest Distance
To find the shortest distance (displacement) between the starting and ending points, the Pythagorean theorem is used. This applies when the movement forms a right-angled triangle.
Formula: Hypotenuse² = Base² + Perpendicular²
(or H² = B² + P²)
Where:
- H (Hypotenuse): The shortest distance between the start and end points.
- B (Base): The horizontal distance covered.
- P (Perpendicular): The vertical distance covered.
Solved Examples
Question: Renu is facing South. She turns 90 degrees left, then she turns 90 degrees right, then she turns 180 degrees left. Now in which direction is she facing?
Question: A nurse moved 90 m in the East in a hospital to look for her duty doctor, then she turned right and went 20m. After this, she turned right and after going 30 m she reached the I.C.U but the Doctor was not there. From there she went 100 m to her north and met her doctor. What is the shortest distance between her starting point and the doctor's location?
Question: On an evening at 4 PM, Seeta and Reema are sitting in a garden facing each other. If Reema's shadow falls behind her, which direction is Seeta facing?