Study the following information carefully and answer the given questions:
A boy who is facing north walks 5 m towards his left from point A and reaches at point B. Now he walks 8 m south direction and reaches at point
Point B is in which direction with respect to H?
C. From point C he takes three consecutive right turns 2 m, 4 m and 7 m respectively and reaches at point G. From point G he takes his right turn and reaches at point H after cover 4 m.
Correct Answer :
North west
Solution :
Correct Answer: North west
Let us trace the step-by-step movement of the boy starting from point A:
1. Point A to Point B:
The boy is initially facing North at point A. He walks 5 m towards his left (West direction) to reach point B.
Relative to A: B is 5 m West of A.
2. Point B to Point C:
From point B, he walks 8 m in the South direction to reach point C.
Relative to B: C is 8 m South of B.
3. Point C to Point G (Three consecutive right turns):
Facing South at C:
- First right turn (West): Walks 2 m. Position is now 2 m West of C.
- Second right turn (North): Walks 4 m. Position is now 4 m North of the previous position.
- Third right turn (East): Walks 7 m to reach point G.
Let us find the coordinates of G relative to B (taking B as origin (0, 0)):
- Position of B = (0, 0)
- Position of C = (0, -8)
- After 2 m West from C = (-2, -8)
- After 4 m North = (-2, -4)
- After 7 m East to point G = (-2 + 7, -4) = (5, -4)
So, Point G is at (5, -4) relative to B.
4. Point G to Point H:
At point G, facing East, he takes a right turn (South) and walks 4 m to reach point H.
- Position of H = (5, -4 - 4) = (5, -8) relative to B.
5. Determining the direction of B with respect to H:
- Point B is at (0, 0).
- Point H is at (5, -8).
- Looking from H (5, -8) to B (0, 0):
To go from H to B, one must move in the negative x-direction (West) and positive y-direction (North).
Therefore, Point B is in the North west direction with respect to Point H.
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