A girl walks straight in the opposite direction of the front door of her…

Concept

In direction-sense problems, track the person’s heading separately from the person’s position. Moving a distance changes location, while an opposite direction or a turn changes the heading.

Use the clockwise compass cycle North → East → South → West → North. A right turn advances one quarter-turn clockwise; a left turn advances one quarter-turn counterclockwise.

Application

1. The door faces south, so walking in the opposite direction makes the girl begin facing north. She walks 50 metres north.

2. While facing north, a left turn changes the heading to west. She then walks 100 metres west.

3. While facing west, a right turn changes the heading to north. Walking the final 100 metres does not change that heading.

Cross-check

Using east as the positive x-axis and north as the positive y-axis, the three movements are (0, 50), (−100, 0), and (0, 100). The last movement vector points north, confirming that the girl is facing North.