You start from a point, follow given directions (North, South, East, West), and determine the final position or shortest distance back to start. The key is visualizing the path and using coordinate geometry or Pythagoras theorem
North is positive Y-axis, East is positive X-axis, South is negative Y-axis, West is negative X-axis. Always draw a rough diagram. Right turn means clockwise rotation (N→E→S→W). Left turn means anticlockwise rotation (N→W→S→E).
SSC asks three main types - (1) Find final position after multiple movements (2) Calculate shortest distance between start and end points (3) Determine direction of final position from starting point. Questions often include multiple turns to confuse students.
Use coordinate method. Place starting point at origin (0,0). Move North = +Y, South = -Y, East = +X, West = -X.
Plot final coordinates and apply distance formula. This eliminates drawing errors.
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.
Students confuse left/right turns with compass directions. Remember that turns are relative to current facing direction, not absolute directions. If facing North and turn right, you face East.
If facing East and turn right, you face South. Always track current facing direction after each turn. Another major error is calculation mistakes in distance formula. Students forget to square the terms or make errors in square root calculation.
Practice mental calculation of common squares: 3²=9, 4²=16, 5²=25, 12²=144, 13²=169. Time-saving tip: Recognize special triangles. 3-4-5 triangle has hypotenuse 5. 5-12-13 triangle has hypotenuse 13. 8-15-17 triangle has hypotenuse 17. If coordinates match these patterns, you can instantly write the answer without calculation.
6graded MCQs · easy to hard · full solution & trap analysis