A woman walks 70 metres south from her house. She then turns left and walks 30…

Concept

Represent a direction problem on a coordinate plane: east is positive x, west is negative x, north is positive y, and south is negative y.

To find the direction back to the starting point, subtract the current coordinates from the starting coordinates and read the signs of the resulting vector.

Application

1. Place the house at (0, 0).

2. Moving 70 metres south gives the position (0, -70).

3. While facing south, a left turn points east; moving 30 metres gives (30, -70).

4. Moving 40 metres north gives (30, -30).

5. The vector from (30, -30) to the house is (0 - 30, 0 - (-30)) = (-30, 30), which combines westward and northward movement.

Cross-check

She is 30 metres east and 30 metres south of the house, so returning requires equal movement west and north. That diagonal direction is North-West.

Therefore, she is walking North-West.