Question Details

A person starts from point A and walks 30 meters in the North direction and then 20 meters towards West and reaches a point B) Thereafter, he takes a southward turn and walks 10 meters to point. C) After that, he turns eastward and covers 15 meters to reach point D) Finally, turning to his right he walks 20 meters. Find the distance from his starting point to the end point.

Options

A

4 meters

B

5 meters 

C

8 meters 

D

10 meters 

Show Answer

Correct Answer :

Option B

5 meters 

Solution :

The correct option is 5 meters.

Let us break down the person's movement step-by-step using a standard coordinate system, where the starting point A is at the origin (0, 0). Let the East-West direction represent the x-axis (East is positive, West is negative) and the North-South direction represent the y-axis (North is positive, South is negative).
Let's trace the positions after each movement:

Step 1: Start at A
Starting position A = (0, 0).

Step 2: Walk 30 meters North
Moving North increases the y-coordinate by 30 meters.
Position is now (0, 30).

Step 3: Walk 20 meters West to reach point B
Moving West decreases the x-coordinate by 20 meters.
Position of point B = (-20, 30).

Step 4: Walk 10 meters South to reach point C
Moving South decreases the y-coordinate by 10 meters.
Position of point C = (-20, 30 - 10) = (-20, 20).

Step 5: Walk 15 meters East to reach point D
Moving East increases the x-coordinate by 15 meters.
Position of point D = (-20 + 15, 20) = (-5, 20).

Step 6: Turn right and walk 20 meters to the final point
At point D, the person is facing East. Turning to his right means turning South.
Walking 20 meters South decreases the y-coordinate by 20 meters.
Final position E = (-5, 20 - 20) = (-5, 0).

Step 7: Find the distance between the starting point A and the final point E
The starting point is A(0, 0) and the final point is E(-5, 0). Since both points lie on the x-axis, the straight-line distance is simply the absolute difference between their x-coordinates:
Distance = |0 - (-5)| = 5 meters.

Thus, the final point is 5 meters to the West of the starting point.

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