A woman in a shopping complex walks 150 m towards the east from her starting position, then turns towards the north and walks 180 m, then turns towards the west and walks 70 m, and finally turns to her left and walks another 180 m. After completing all these moves, where is she now with reference to her original starting position in terms of distance and direction?

Introduction / Context:
This question involves a sequence of rectangular movements and a final left turn in a shopping complex. The goal is to determine the net displacement of the woman from her starting point, not the total path length she has walked. It requires keeping track of the horizontal and vertical components and understanding the effect of turns on direction.

Given Data / Assumptions:

• The woman walks 150 m east from her starting position.
• She then turns north and walks 180 m.
• Next, she turns west and walks 70 m.
• Finally, she turns to her left and walks 180 m.
• Left is defined relative to the direction in which she is currently facing.
• All paths are straight and on flat ground.

Concept / Approach:
We employ a coordinate system where east west affects the horizontal axis and north south affects the vertical axis. Turning to the left rotates the direction 90 degrees anticlockwise. After calculating the final coordinates, we compare them to the starting coordinates to find the net displacement, which gives both magnitude and direction of her final position relative to the origin.

Step-by-Step Solution:
Step 1: Start at (0, 0). Walking 150 m east takes her to (150, 0). Step 2: She then turns north and walks 180 m, reaching (150, 180). Step 3: Next, she turns west and walks 70 m, reducing the horizontal coordinate to 150 − 70 = 80, giving the position (80, 180). Step 4: At this moment she is facing west. A left turn from west makes her face south. She then walks 180 m south, reducing the vertical coordinate from 180 to 0. The final position becomes (80, 0). Step 5: Comparing (80, 0) with the starting point (0, 0) shows that she is 80 m east of her original position with no north south displacement.

Verification / Alternative check:
Consider the north south movements: she walks 180 m north and then 180 m south, so these cancel, leaving zero net north south movement. For east west movements, she walks 150 m east and 70 m west, resulting in a net eastward displacement of 80 m. This simple balancing check confirms the coordinate calculation and reinforces the understanding that cancelling movements is key in such problems.

Why Other Options Are Wrong:
The options 80 m west and 220 m west incorrectly reverse the direction or combine distances in an incorrect way. The option 220 m east looks like a sum of some segments rather than a net result. None of these match the calculated net displacement of 80 m east from the origin.

Common Pitfalls:
Typical errors include misinterpreting the final left turn from west, leading to a wrong final direction, and forgetting that equal north and south movements cancel each other. Some also add distances without considering opposing directions. Careful diagramming and stepwise calculation prevent these mistakes.

Final Answer:
She is now located 80 m east of her starting position.