Direction TestMTP Dec 22 Series IIQuestion 2236 of 165
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Shweta moved a distance of 75m towards the north. She then turned to the left and walked about 25m, turned left again and walked 80m. Finally, she turned to the right at an angle of 45∘\displaystyle 45^\circ. In which direction was she moving finally?

Options

ASouth
BSouth-West
CNorth-East
DNorth-West
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Correct Answer

✅ Option b — South-West

All Options:

  • ASouth
  • BSouth-West
  • CNorth-East
  • DNorth-West

Detailed Solution & Explanation

Let Shweta start at the origin (0,0)\displaystyle (0, 0) facing North. Left turns correspond to counter-clockwise (+), and right turns correspond to clockwise (-).
1. **First Segment (North)**: She moves 75\displaystyle 75 meters North. Coordinates: P1=(0,75)\displaystyle P_1 = (0, 75). Direction: North.
2. **Second Segment (Left Turn / West)**: Facing North, a left turn points West. She walks 25\displaystyle 25 meters West. Coordinates: P2=(−25,75)\displaystyle P_2 = (-25, 75). Direction: West.
3. **Third Segment (Left Turn / South)**: Facing West, a left turn points South. She walks 80\displaystyle 80 meters South. Coordinates: P3=(−25,75−80)=(−25,−5)\displaystyle P_3 = (-25, 75 - 80) = (-25, -5). Direction: South.
4. **Final Turn (45° Right)**: From facing South (direction vector −j^\displaystyle -\hat{j}), she turns right (clockwise, towards West −i^\displaystyle -\hat{i}) by 45∘\displaystyle 45^\circ. The resulting direction vector is:
v⃗=−sin⁡(45∘)i^−cos⁡(45∘)j^\displaystyle \vec{v} = -\sin(45^\circ)\hat{i} - \cos(45^\circ)\hat{j}
Since both the x\displaystyle x and y\displaystyle y components are negative, she is moving in the South-West direction.

Thus, she is moving in the South-West direction finally.
Hence, **Option B** is the correct answer.

More Questions from Direction Test

A man stands on a point and starts walking towards North then turns left then turns right and then left in which direction he is moving.

Rahim started from point X and walked straight 5\displaystyle 5 km west, then turned left and walked straight 2\displaystyle 2 km, then again turned left and walked straight 7\displaystyle 7 km. In which direction is he from the point X?

Manu wants to go to the market. He starts from his house towards North and reaches a crossroad after 30\displaystyle 30m. He turns towards East, goes 10\displaystyle 10m till the second crossing and turns again, moves towards South straight for 30\displaystyle 30m where marketing complex exits. In which direction is the market from his house?

A man is facing North-West. He turns 90° in the clockwise direction, then 180° in the anticlockwise direction and then another 90° in the same direction. Which direction is he facing now?

Rajni walked 20 m towards the North. Then she turned right and walks 30 m. Then she turns right and walks 35 m. Then she turns left and walks 15 m. Finally she turns left and walks 15 m. In which direction and how many meters is she from the starting position?

At a crossing, there was a direction pole, which was showing all the four correct directions. But due to the wind, it turns in such a manner that now West pointer is showing South. Harish went in the wrong direction thinking that he was travelling East. In which direction he was actually travelling?

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