A girl is facing north. She turns 90° in the anti-clockwise direction and then 45° in the clockwise direction. Which direction is she facing now?
North-West
Understanding Directional Turns
This question involves understanding how turns, specifically clockwise and anti-clockwise turns, affect the direction a person is facing. We start with a known direction and apply the given turns step-by-step.
Step-by-Step Direction Change Analysis
Let's break down the movement:
- Starting Direction: The girl is initially facing North.
- First Turn: She turns $90^{\circ}$ in the anti-clockwise direction from North.
- Think of the directions like a compass or clock face. Starting from North, an anti-clockwise turn moves towards West.
- $90^{\circ}$ anti-clockwise from North points exactly towards West.
- After the first turn, the girl is facing West.
- Second Turn: She then turns $45^{\circ}$ in the clockwise direction from her current direction (West).
- From West, a clockwise turn moves back towards North.
- A $90^{\circ}$ clockwise turn from West would take her back to North.
- A $45^{\circ}$ clockwise turn is half of a $90^{\circ}$ turn. It will take her halfway from West back towards North.
- The direction halfway between West and North is North-West.
Therefore, after both turns, the girl is facing North-West.
Final Direction Determination
By carefully following the initial direction and applying each turn sequentially, we determined the final direction.
- Start: North
- Turn 1 ($90^{\circ}$ Anti-clockwise): North $\rightarrow$ West
- Turn 2 ($45^{\circ}$ Clockwise from West): West $\rightarrow$ North-West
The final direction she is facing is North-West.
| Step | Action | Direction Change | Resulting Direction |
|---|---|---|---|
| Start | Initial position | N/A | North |
| Turn 1 | $90^{\circ}$ Anti-clockwise | North $\rightarrow$ West | West |
| Turn 2 | $45^{\circ}$ Clockwise | West $\rightarrow$ North-West | North-West |
Revision Table: Key Directional Concepts
| From Direction | Turn | Resulting Direction Examples |
|---|---|---|
| North | $90^{\circ}$ Clockwise | East |
| North | $90^{\circ}$ Anti-clockwise | West |
| East | $90^{\circ}$ Clockwise | South |
| East | $90^{\circ}$ Anti-clockwise | North |
| North | $45^{\circ}$ Clockwise | North-East |
| North | $45^{\circ}$ Anti-clockwise | North-West |
Additional Information: Angles and Directions
Understanding the angles between cardinal and intercardinal directions is helpful for solving these types of problems:
- The angle between two adjacent cardinal directions (like North and East) is $90^{\circ}$.
- The angle between a cardinal direction and an adjacent intercardinal direction (like North and North-East) is $45^{\circ}$.
- A full circle is $360^{\circ}$.
- Clockwise rotation is the same direction as the hands of a clock move.
- Anti-clockwise (or counter-clockwise) rotation is the opposite direction of the hands of a clock.
These concepts allow you to visualize or calculate the final direction after a series of turns.
Important Questions from Direction Sense Test
A man moves to the east side, then turns left, then right, and then further turns right again and then moves left. Now, in which direction is the man?
Sunita rode her scooty Northward, then turned left and then again rode to her left 4 km. She found herself exactly 2 km. West to her starting point. How far did she ride Northwards initially?
Pinky walks a distance 600m towards east, turns left moves 500m, then again turns left and walks 600m and then turns left again and moves 500m and halts. At what distance (in meters) is she from the starting point?
One evening before sunset, two friends Shahrukh and Rakesh were talking to each other face-to-face. If Rakesh’s shadow is exactly to his right side, which direction was Shahrukh facing?
A boy runs 4 km to East side, then turns right and runs 6 km, and then turns left and runs 8 km. Again turns left to run 3 km, again turns right 4 km, then turns right 1 km. Now the boy is in which direction?
