A girl walks 30 m North-West, then 30 m South-West, then 30 m South-East. She now turns toward her home (starting point). In which direction is she moving?

Introduction / Context:
This problem uses diagonal moves (NW, SW, SE), which combine North/South and East/West components. The key is to decompose each diagonal step into orthogonal components and sum them to find the resultant displacement. The direction toward home is the direction opposite to her displacement vector.

Given Data / Assumptions:

• Step 1: 30 m North–West (equal parts North and West).
• Step 2: 30 m South–West (equal parts South and West).
• Step 3: 30 m South–East (equal parts South and East).
• North and East are taken as positive axes; South and West as negative.

Concept / Approach:
Resolve each 30 m diagonal into components 30/√2 ≈ 21.21 m along each axis. Add signed components to find the total displacement (x, y). The direction toward home is the heading from the current point back to the origin, i.e., opposite of (x, y).

Step-by-Step Solution:

Verification / Alternative check:
Create a quick sketch with three equal-length diagonals; you will see the endpoint lies in the South-West quadrant relative to start, so moving toward home must be North-East.

Why Other Options Are Wrong:

• South–West and South–East point away from home given the net SW displacement.
• North–West does not reverse both components; only NE reverses both signs.

Common Pitfalls:
Forgetting that NW, SW, SE are 45° diagonals with equal magnitude components, or reversing axes when summing vectors.

Final Answer:
North–East