Direction & Distance

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).

Ram starts from home, walks 4km North, then 3km East, then 2km South. Find shortest distance to reach home

Place home at (0,0)

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

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

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

3²=9, 4²=16, 5²=25, 12²=144, 13²=169

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.