Map Direction Rotation Explained
This question involves understanding how directions change when a map is rotated. We need to figure out the new direction of Northeast after a specific rotation is applied.
Understanding the Rotation
The problem states that the map is placed such that the direction 'East' now points towards 'Southeast'. Let's analyze this change:
- The standard direction 'East' corresponds to 90 degrees on a compass (assuming North is 0 degrees).
- The new direction 'Southeast' corresponds to 135 degrees on a compass.
- The difference between the new direction and the original direction is:
$135 \text{ degrees} - 90 \text{ degrees} = 45 \text{ degrees}$ - Since Southeast is clockwise from East, the map has been rotated by 45 degrees clockwise.
Applying Rotation to Northeast
Now we need to find out where 'Northeast' will point after this 45-degree clockwise rotation.
- The standard direction 'Northeast' corresponds to 45 degrees on a compass (midway between North at 0 degrees and East at 90 degrees).
- We apply the same rotation of 45 degrees clockwise to this direction.
- New angle = Original angle of Northeast + Rotation angle
New angle = $45 \text{ degrees} + 45 \text{ degrees} = 90 \text{ degrees}$ - The direction corresponding to 90 degrees on a compass is East.
Conclusion
Therefore, if the map is rotated so that East becomes Southeast, the Northeast direction will become East.
Important Questions from Direction and Distance (Notes)
- A woman leaves her home. She walks 40 m in North-West direction and then 90 m in South-East direction. Then, she moves 30 m in North direction. How far is she now from her initial position ?
- N sits to the North of L and West of M. L sits to the East of O. If everyone is facing North, which direction of O, is N?
I starts from Point A and drives 5 km towards the north. He then takes a right turn, drives 2 km, turns right and drives 9 km. He then takes a right turn and drives 7 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are $90^\circ$ turns only unless specified.)
A tourist drives $20 \text{ km}$ towards east, turns right and drives $6 \text{ km}$, then drives $6 \text{ km}$ towards west. He then turns to his left and drives $4 \text{ km}$ and finally turns right and drives $14 \text{ km}$. Where is he from his starting point?
- A Couple started to their offices in the morning from their home. While husband drives 3 km South and then 2 km to his right to reach his office, wife goes 2 km towards East for her office. With respect to husband's office, how far and in which direction is the wife's office ?
