Ram starts from home, walks 4km North, then 3km East, then 2km South. Find shortest distance to reach home.
Solution: Place home at (0,0). After 4km North: (0,4).
After 3km East: (3,4). After 2km South: (3,2). Final position = (3,2).
Shortest distance = √[(3-0)² + (2-0)²] = √[9+4] = √13 = 3.6km
Worked Example 2: Sita walks 5km East, turns right, walks 12km, turns right again, walks 5km. How far is she from start?
Solution: Start at (0,0). 5km East: (5,0). Turn right (now facing South), walk 12km: (5,-12).
Turn right again (now facing West), walk 5km: (0,-12). Distance from start = √[(0-0)² + (-12-0)²] = 12km
Advanced Shortcut: For rectangular paths, if you return to same X or Y coordinate, the distance equals the remaining coordinate value. In example 2, X-coordinate returned to 0, so distance = Y-coordinate = 12km.
Direction Shortcut: Final direction from start can be found using coordinates.
If final position is (a,b), then direction is determined by signs: (+,+) = Northeast, (+,-) = Southeast, (-,+) = Northwest, (-,-) = Southwest.