From point A, Ram moves 100m in north-east direction, he again turns and moves 100m in south-east direction. He again turns and covers 100m south-west and finally covers 100m in north-west direction. In which direction is he now with respect to A?
- AWest
- BSouth-west
- CAt point A
- DEast
Solution & Step-by-step Explanation
Let's plot Ram's movements step by step starting from the origin A(0,0):
Move 1: 100m North-East
This path moves diagonally upwards and to the right.
Move 2: 100m South-East
Turning 90
∘
clockwise, he moves diagonally downwards and to the right.
Move 3: 100m South-West
Turning another 90
∘
clockwise, he moves diagonally downwards and to the left.
Move 4: 100m North-West
Turning another 90
∘
clockwise, he moves diagonally upwards and to the left.
Since all four paths are equal in length (100m) and form consecutive perpendicular directions, they trace a perfect square tilted at 45
∘
. The final movement brings him precisely back to his starting position, Point A.
Move 1: 100m North-East
This path moves diagonally upwards and to the right.
Move 2: 100m South-East
Turning 90
∘
clockwise, he moves diagonally downwards and to the right.
Move 3: 100m South-West
Turning another 90
∘
clockwise, he moves diagonally downwards and to the left.
Move 4: 100m North-West
Turning another 90
∘
clockwise, he moves diagonally upwards and to the left.
Since all four paths are equal in length (100m) and form consecutive perpendicular directions, they trace a perfect square tilted at 45
∘
. The final movement brings him precisely back to his starting position, Point A.