Rita travels 35 kilometres from a certain point towards the south. She then turns left and travels 20 kilometres. Finally, she turns left again and travels another 35 kilometres. In which direction is Rita now located from her original starting point?

Introduction / Context:
Direction sense questions like this one require you to mentally or graphically track the path of a person as they move in steps with given distances and turns. The main target here is not the distance but the direction of the final position relative to the starting point. This problem uses two left turns after the initial southward movement, creating a rectangular path that is easy to follow if you draw a rough figure or use coordinate reasoning.

Given Data / Assumptions:

• Rita starts at a fixed point, which we can treat as the origin.
• She travels 35 kilometres towards the south.
• She then turns left and travels 20 kilometres.
• Lastly, she turns left again and travels 35 kilometres.
• All turns are perpendicular (right angles).
• We must find the compass direction from the starting point to her final position.

Concept / Approach:
To solve, we can use a coordinate system where south corresponds to negative y, north to positive y, east to positive x and west to negative x. Each leg of Rita's journey updates her coordinates based on the current facing direction and the distance travelled. After calculating the final coordinates, we compare them to the origin. If the final x coordinate is positive and the y coordinate is zero, she is directly east of the starting point, and similar logic holds for other directions.

Step-by-Step Solution:
Step 1: Let Rita start at point O with coordinates (0, 0), facing south for the first movement. Step 2: She travels 35 kilometres south, so her position becomes (0, -35). Step 3: From facing south, a left turn makes her face east. She then travels 20 kilometres east to reach (20, -35). Step 4: From facing east, another left turn makes her face north. She travels 35 kilometres north to reach (20, 0). Step 5: The final coordinates are (20, 0). The x coordinate is positive and the y coordinate is zero. Step 6: A point with positive x and zero y lies directly to the east of the origin, so Rita is east of her starting point.

Verification / Alternative check:
We can also solve this geometrically without coordinates. The first and third movements are both 35 kilometres and are exactly opposite in direction (south then north), so they cancel each other vertically, bringing her back to the same north-south line as the starting point. During the middle movement of 20 kilometres east, she shifted horizontally from the original line and never returned in the opposite horizontal direction. Thus, at the end, she must be 20 kilometres directly east of the starting point, confirming the direction as east.

Why Other Options Are Wrong:

• Option B, West, would require Rita to move in the opposite horizontal direction, which she never does.
• Option C, North, would require a final y coordinate greater than zero, but the north and south movements cancel each other out.
• Option D, South, would be correct only if there were more southward movement than northward, which is not the case here.
• Option E, North-East, is wrong because her vertical displacement is zero, so there is no northward component in her final position.

Common Pitfalls:
Students often forget that equal distances in opposite directions cancel out. Another common mistake is misidentifying left and right when the person is facing south or west, rather than north. Visualising or sketching the path step by step, or using arrows on paper, can greatly reduce confusion. Always check both horizontal and vertical components before deciding the final direction.

Final Answer:
Rita ends up directly to the East of her starting point.