From point X, a person walks 45 m towards the east. He then takes a left turn and walks 40 m. He then takes a right turn and walks 90 m. He then takes a right turn and walks 60 m. Finally, he takes a right turn and walks 135 m to reach point Y. How far and in which direction is point X from point Y? (All turns are 90 degree turns only)

Explanation

Given: A person starts at point X and makes several turns while walking certain distances. We need to find the distance and direction from point Y back to point X. Let’s track the person’s path based on the given directions: 1. From point X: Walk 45 m east. Position after this step: 45 m east of X. 2. Left turn: Walk 40 m north. Position after this step: 45 m east and 40 m north of X. 3. Right turn: Walk 90 m east. Position after this step: (45 + 90) m = 135 m east and 40 m north of X. 4. Right turn: Walk 60 m south. Position after this step: 135 m east and (40 - 60) m = -20 m (20 m south) of X. 5. Right turn: Walk 135 m west. Position after this step: (135 - 135) m = 0 m east (directly west) and 20 m north of X. Final Position Relative to Point X The person ends up 20 m north of the starting point X. Final Answer Point Y is 20 meters north of point X.