Question

A person starts walking towards the east and covers a distance of \(4\) km. Then, the person turns right and walks \(3\) km. After that, the person turns left and covers \(5\) km. Finally, the person turns left again and walks \(2\) km. In which direction is the person now with respect to the starting point?

• A. North
• B. South
• C. East
• D. West

Hint:

In direction problems, convert each segment into coordinate moves. “Right” from East is South; “Left” from South is East, etc. Summing \(x\) and \(y\) shifts gives the final direction.

Answer 1

The Correct Option is C

Solution:
Step 1 (Set axes and initial direction).
Let the starting point be the origin \(O(0,0)\). Take \(+\!x\) as East and \(+\!y\) as North.
Step 2 (Track each move using coordinates).
1) Walk \(4\) km East: position \(P_1(4,0)\).
2) Turn right from East \(\) face South; walk \(3\) km: \(P_2(4,-3)\).
3) Turn left from South \(\) face East; walk \(5\) km: \(P_3(9,-3)\).
4) Turn left from East \(\) face North; walk \(2\) km: \(P_4(9,-1)\).
Step 3 (Net displacement and direction).
From \(O(0,0)\) to \(P_4(9,-1)\): \(+\!9\) km East, \(1\) km South. Thus the person lies mostly to the East (slightly to the South) of the start. With given pure-cardinal options, the direction relative to the start is East.
\[ {\text{East (Option (c)}} \]