Direction sense for LIC AAO

Direction sense is one of the few reasoning topics where a single method works for every question. Candidates who trace paths mentally lose track after the third turn. Candidates who write coordinates never do. Each move becomes an addition to x or y, and the final distance comes from Pythagoras. Learn the method once and these questions take under a minute, even with five turns.

The coordinate method

1. Start at (0, 0). East is +x, west is −x, north is +y and south is −y.
2. Track which way the person faces after every turn.
3. Add each distance to x or y according to the facing direction.
4. At the end, the distance from the start is √(x² + y²).
5. Read the direction from the signs: x > 0 and y > 0 is north-east, x < 0 and y < 0 is south-west, and so on. If x or y is zero, the direction is a pure one: north, south, east or west.

Turn table

A right turn is 90° clockwise and a left turn is 90° anticlockwise, whichever way the person faces. Do not picture yourself turning. Use the table.

Turns in degrees

Give each direction a bearing, measured clockwise from north: N = 0°, NE = 45°, E = 90°, SE = 135°, S = 180°, SW = 225°, W = 270°, NW = 315°.

• A clockwise turn adds degrees.
• An anticlockwise turn subtracts degrees.
• Add or subtract 360 to bring the answer between 0° and 359°.

Shadows

• Morning: the sun is in the east, so shadows fall to the west.
• Evening: the sun is in the west, so shadows fall to the east.
• Noon: the sun is roughly overhead, so shadow questions almost always use morning or evening.

Once you know where the shadow falls, use the facing direction to decide whether that is the person's left, right, front or back.

Worked examples

Example 1. Walk 20 m east, turn left and walk 15 m. Where are you from the start?

• East 20 → (20, 0). Left from east is north: 15 → (20, 15).
• √(400 + 225) = √625 = 25 m, north-east.

Example 2. From P, walk 7 m north, turn right and walk 4 m, then turn right and walk 7 m. Where are you from P?

• North 7 → (0, 7). Right is east: (4, 7). Right again is south: (4, 0).
• 4 m east of P.

Example 3. Walk 10 m north, turn left and walk 6 m, turn left and walk 18 m, turn left and walk 12 m. Where are you from the start?

• North 10 → (0, 10). Left is west: (−6, 10). Left is south: (−6, −8). Left is east: (6, −8).
• √(36 + 64) = √100 = 10 m, south-east.

Example 4. In the evening, a person faces north. On which side does their shadow fall?

• Evening shadows fall east. Facing north, east is on the right.
• To their right.

Example 5. A person faces west, turns 90° clockwise, then 135° anticlockwise, then 180°. Which way do they face now?

• West = 270°. +90 = 360°, which is 0°, north. −135 = −135°, which is 225°, south-west. +180 = 405°, which is 45°.
• North-east.

Coded direction questions

Mains-level sets sometimes hide the directions behind symbols. Suppose P @ Q means P is 4 m east of Q, and P % Q means P is 3 m north of Q. What does A @ B % C tell you about A and C?

• Split at each symbol: A @ B and B % C.
• Put C at (0, 0). B is 3 m north of C: (0, 3). A is 4 m east of B: (4, 3).
• √(16 + 9) = 5. A is 5 m north-east of C.

The method is the same as before. Decode every symbol first, fix the last-named person at the origin, and work backwards along the chain.

Practice set

1. Walk 9 m south, then 12 m west. How far and in which direction are you from the start?
2. Someone facing south turns right twice. Which way do they face?
3. In the morning, a person's shadow falls directly behind them. Which way are they facing?
4. Walk 5 km west, turn right and walk 3 km, turn right again and walk 9 km. How far and in which direction are you from the start?
5. A person faces north-east and turns 135° clockwise. Which way do they face?
6. Q is 6 m north of P. R is 8 m west of Q. S is 12 m south of R. Where is S with respect to P?
7. In the morning, a person's shadow falls to their left. Which way are they facing?
8. In the evening, a person's shadow falls to their left. Which way are they facing?

Answers

1. 15 m, south-west. (−12, −9); √(144 + 81) = √225 = 15.
2. North. South → right → west → right → north.
3. East. Morning shadows fall west; if west is behind them, they face east.
4. 5 km, north-east. West 5 → (−5, 0). Right from west is north: (−5, 3). Right from north is east: (4, 3). √(16 + 9) = 5.
5. South. 45° + 135° = 180°.
6. 10 m, south-west. Q (0, 6), R (−8, 6), S (−8, −6). √(64 + 36) = 10.
7. North. Morning shadows fall west. West is on the left of someone facing north.
8. South. Evening shadows fall east. East is on the left of someone facing south.

A quick routine

• Write (0, 0) and the first facing direction before reading the second move.
• After each turn, write the new facing direction as a single letter: N, E, S or W.
• Check whether the question asks from the start or from the end.
• Look for Pythagorean triples: 3–4–5, 6–8–10, 5–12–13, 8–15–17, 9–12–15. Most distance answers use one.

What to do next

• Do ten direction questions using coordinates only, with no mental tracing, and time them.
• Carry the same left–right discipline into seating arrangements.
• Add direction sense to your week 1 quick topics in the reasoning plan.