A woman first walks 3 km towards the north from her starting position, then turns towards the west and walks 4 km, after that she turns towards the south and walks 7 km, and finally she turns to her left and walks another 4 km. Based on this sequence of movements, where is she now with reference to her original starting position and which direction and distance describe her final location?

Introduction / Context:
This question evaluates understanding of basic direction sense and net displacement. The woman makes several moves in different directions, and we are asked to find her final position relative to the starting point, not the total distance that she has walked. Solving this requires careful tracking of movements along the north south and east west axes, and recognising that some movements cancel out partially or fully.

Given Data / Assumptions:

• The woman walks 3 km towards the north from her starting point.
• She then turns west and walks 4 km.
• Next, she turns south and walks 7 km.
• Finally, she turns to her left and walks 4 km.
• Left and right are with respect to the direction in which she is currently facing at that moment.
• All paths are straight and on level ground, and distances are accurate.

Concept / Approach:
We break her path into horizontal (east west) and vertical (north south) components. Movements towards the north are considered positive on the vertical axis, movements towards the south negative. Movements towards the east are positive on the horizontal axis, and movements towards the west are negative. After each segment we update the position. At the end we compare the final coordinates with the starting point to determine the net displacement in both magnitude and direction.

Step-by-Step Solution:
Step 1: Start at the origin (0, 0). After walking 3 km north, her position becomes (0, 3). Step 2: From there she turns west and walks 4 km. Moving west decreases the horizontal coordinate, so the new position is (−4, 3). Step 3: She then turns south and walks 7 km. Moving south reduces the vertical coordinate by 7, so the new position is (−4, 3 − 7) = (−4, −4). Step 4: At this moment she is facing south. Turning left from south means she will face east. She now walks 4 km east. Moving 4 km east increases the horizontal coordinate by 4, so the new position is (−4 + 4, −4) = (0, −4). Step 5: Her final coordinates are therefore (0, −4). The starting point was (0, 0). So she is 4 km south of her starting position.

Verification / Alternative check:
Notice that she moved 3 km north and later 7 km south. The net vertical movement is 7 − 3 = 4 km south. For horizontal movement, she walked 4 km west and later 4 km east, which cancel each other, leaving zero net horizontal displacement. So the only remaining net effect is 4 km towards the south, which confirms that she is exactly 4 km south of her starting point.

Why Other Options Are Wrong:
The option 10 km south is wrong because it adds some distances instead of considering cancellation. The options 4 km north and 10 km north reverse the direction and ignore that she walked a greater distance south than north. They do not represent the correct net movement. Hence only 4 km south matches the calculated displacement.

Common Pitfalls:
A common mistake is to confuse total distance travelled with displacement. Another typical error is to misinterpret the final left turn, especially when turning from south. Some test takers also forget to cancel equal east and west movements. Drawing a simple diagram with arrows or using a small coordinate system on paper significantly helps in avoiding these pitfalls.

Final Answer:
The woman is now located 4 km south of her original starting position.