7. A hiker walks 2 km south, then turns west and walks for 4 km, then he turns north and walks
for 5 km, then he turns to his right and walks for 4 km. where is he now with respect to his
starting position?
To determine the hiker's location with respect to his starting position, we can use the positioning given in terms of cardinal directions.
The hiker first walks 2 km south, which means he moves 2 km in the opposite direction of north. This brings him 2 km to the south of his starting position.
He then turns west and walks for 4 km. This means he moves 4 km in the opposite direction of east. Since he was initially south of his starting position and moves to the west, the hiker is now 4 km west and 2 km south of his starting position.
Next, the hiker turns north and walks for 5 km. This means he moves 5 km in the opposite direction of south. Since he was initially 4 km west and 2 km south of his starting position and now moves north, the hiker is now 4 km west and 3 km north of his starting position.
Finally, the hiker turns right, which means he turns towards the east, and walks for 4 km. This means he moves 4 km in the east direction. Since he was initially 4 km west and 3 km north of his starting position and now moves east, the hiker is now at the same latitude (3 km north) and 1 km east of his starting position.
Therefore, the hiker is 1 km east and 3 km north of his starting position.