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 to determine the relative positions of all the points on a standard directional plane (where North is Up, South is Down, East is Right, and West is Left):
Step 1: Movement from Point A to Point B
The boy starts at point A facing North.
He turns to his left (which corresponds to West) and walks 5 m to reach point B.
Therefore, point B is located 5 m West of point A.
Step 2: Movement from Point B to Point C
From point B, he walks 8 m in the South direction to reach point C.
Therefore, point C is 8 m South of point B.
Step 3: Three consecutive right turns (from Point C to Point G)
While at point C, he is facing South.
1. First right turn (2 m): Turning right from South means facing West. He walks 2 m West to reach an intermediate point.
2. Second right turn (4 m): Turning right from West means facing North. He walks 4 m North to reach another intermediate point.
3. Third right turn (7 m): Turning right from North means facing East. He walks 7 m East to reach point G.
Let us analyze the position of point G relative to point C:
Net horizontal displacement from C: 2 m West + 7 m East = 5 m East.
Net vertical displacement from C: 4 m North.
So, Point G is located 5 m East and 4 m North of point C.
Step 4: Movement from Point G to Point H
At point G, he was moving East, so he is facing East.
He turns right (which corresponds to South) and walks 4 m to reach point H.
Since point G was 4 m North of the horizontal line containing point C, walking 4 m South brings point H exactly onto the same horizontal line (East-West line) as point C.
Therefore, Point H is 5 m East of Point C.
Step 5: Determining the position of Point B with respect to Point H
Let us place Point H at coordinates :
Since Point H is 5 m East of Point C, Point C is located 5 m West of Point H, i.e., at coordinates .
Since Point B is 8 m North of Point C (since C was 8 m South of B), the coordinates of Point B are:
Horizontal coordinate: 5 m West of H ()
Vertical coordinate: 8 m North of H ()
Thus, relative to Point H, Point B is in the North direction and West direction.
Hence, Point B is in the North west direction with respect to Point H.
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