Direction & Distance
🔒 Log in to trackDirection faced and net direction
🔒 Log in to trackTwo sub-formats:
- Which direction is X facing now? — pure turn-tracking. A clock-wise turn of 90° maps N→E→S→W→N; anticlockwise runs N→W→S→E→N. An about-turn adds 180°. Turn, update the heading, repeat.
- In which direction is the endpoint from the start? — finish the walk, note the final (x, y), and read the direction from signs: (+x, +y) = North-East, (−x, +y) = North-West, (+x, −y) = South-East, (−x, −y) = South-West; a zero component drops that word.
Both take seconds if you write the heading after every turn instead of trusting memory across three turns.
Detailed notes
Where is he facing, and in what direction is the endpoint
Two different questions live in this subtopic, and they need different tools.
Question type 1: final facing. The walker starts facing some direction and turns. Only the turns matter — distances are decoration. Use the quarter-turn count:
- One right turn = +90° clockwise; one left turn = −90° (anticlockwise); "about turn"/180° = two quarter turns.
- Net turn = (rights − lefts) mod 4. Then read the result off the cycle N → E → S → W → N (clockwise).
Example: facing West, turns 90° anticlockwise then 270° clockwise. Net = −1 + 3 = +2 quarter turns → W + 2 = E. He faces East.
Question type 2: direction of the endpoint from the start. Here the walking path matters, the facing does not. Net the moves exactly as in distance questions (net E, net N) and read the compass of the point (net E, net N):
- E > 0, N = 0 → East; E < 0, N = 0 → West; N > 0, E = 0 → North; N < 0, E = 0 → South.
- Both nonzero → combined word: (E>0, N>0) North-East, (E>0, N<0) South-East, (E<0, N>0) North-West, (E<0, N<0) South-West.
"Direction of B from A" always means: stand at A, look at B, name the compass word. Reverse the pair and the word flips to its opposite (NE ↔ SW).
Turns while walking. Sentences like "walks 5 km, turns left, walks 3 km" need you to track facing leg by leg, because 'left' depends on the current facing. Walk it on paper: arrow out, turn the arrow, next arrow. After the final leg, the direction the last arrow points is the final facing; the straight line from the very start to the final point is the displacement direction.
Backtracking. "Turns back / retraces / returns" = 180°: the walker now faces the opposite direction and any new leg cancels the old one metre for metre.
The two-second sanity check. After computing, look at the sketch: a person who ended North and East of the start cannot be 'South-West' from it; a walker who never left the North-South line cannot be 'North-East'. Ten seconds of picture-checking catches most sign slips before they cost a mark.
Mixed questions. The hardest questions in this subtopic combine both tools: a walk with mid-path turns (facing tracked leg by leg) and then "in which direction is the endpoint from the start" (net the legs, ignore the facings). Do the two parts with two separate lists — an arrow chain for the facings and a leg tally for the displacement — and never try to read one off the other.
Quick revision
- Final facing: net quarter turns = rights − lefts (mod 4), read on the N→E→S→W cycle.
- Endpoint direction: net (E, N) → one of the 8 compass words; ignore distances.
- "X from Y" = stand at Y, look at X; swapping the pair flips the word.
- Track facing leg by leg when turns come mid-walk; the page never rotates.
- 180° turn reverses both facing and direction of travel.
Types of questions asked
Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.
Type 1: Net quarter-turns for final facingvery common3 practice Q
A start facing plus a list of turns (left/right/180°); question: which direction is he facing now?
- Right = +1 quarter turn, left = −1, 180° = +2 (or −2, same thing mod 4).
- Sum the turns mod 4.
- Move that many steps on the clockwise cycle N → E → S → W.
Why it works: each quarter turn is 90° and the four compass points close a cycle.
Example: Facing West, a man turns 90° anticlockwise, then 270° clockwise. Which direction is he facing?
Net = −1 + 3 = +2 quarter turns → W + 2 = East.
Type 2: Endpoint direction from the startvery common2 practice Q
A walking path; question asks the direction of the final point from the starting point (not the facing).
- Net the legs into (E, N) — facing never matters here.
- Zero in one component → pure N/S/E/W; both nonzero → combined NE/NW/SE/SW word.
- Sign check: E>0 = East, N>0 = North.
Why it works: 'direction of the endpoint from start' is the compass word of the displacement vector.
Example: A woman walks 4 km North and 3 km East. In which direction is she from her start?
Net (3 E, 4 N) → North-East.
Type 3: Left/right turns mid-walkcommon2 practice Q
'Walks 5 km, turns left, walks 3 km...' — the turn word is relative to the current walking direction.
- Track the current heading arrow leg by leg.
- 'Left' = 90° anticlockwise of the current arrow; 'right' = 90° clockwise.
- Draw each leg as a new arrow, then answer from the drawing.
Why it works: the walker rotates; only the arrow chain on paper keeps the geometry honest.
Example: Walking North, Ravi turns left and walks 3 km, then turns left again and walks 5 km. Which direction is the last leg?
N → left → W → left → South.
Type 4: About-turn and return legscommon2 practice Q
'Turns back / retraces his path / returns' appears in the middle of a walk.
- A 180° turn flips the facing to its opposite.
- New legs after the flip cancel old legs along the same line.
- Final facing = opposite of the direction before the flip.
Why it works: retracing walks the same line in the opposite sense.
Example: A man walks 6 km East, then turns back and walks 2 km. Which direction is he facing, and how far is he from the start?
Facing flips E → West; position 6 − 2 = 4 km East of the start.
Formulas
Every right turn moves one step along this cycle.
Every left turn moves one step along this cycle.
Signs of the net components give the quadrant.
Shortcut tricks
⚡ Write the heading down each time
After every turn, overwrite a single letter (N/E/S/W). Three written letters beat one mental chain — and if a wrong option appears, each written heading is checkable.
Example: Q. Facing West, a man turns 90° clockwise, then 180° anticlockwise. Final facing?
Sol. W --90° CW--> N --180° ACW--> South.
One letter, overwritten per turn.
Where students lose marks
Applying 'left = West' regardless of current facing.
Counting a 180° turn as two separate questions' worth of turns.
Reading the final facing when the question asks direction-from-start (or vice versa).
Practice sets — 14 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 10 questions
Suggested time 7 min · wrong answers go to your mistake notebook automatically.