Direction sense for AFCAT: turns, distances and shadows, drawn step by step

Direction sense questions describe a walk, a drive or a flight path in words and ask where someone ends up, how far they are from the start, or which way they are facing. The arithmetic is school-level. What costs marks is losing track of a turn halfway through, or answering the direction the wrong way round.

For an Air Force aspirant this topic is also a small rehearsal of a real skill: keeping a mental map while a heading changes. The fix is the same in both places. Draw it. Every step, on the rough sheet, with north at the top.

The compass you need

There are four main directions and four in between.

Thinking in angles makes turn questions mechanical. A clockwise turn adds degrees; an anticlockwise turn subtracts them. Wrap around at 360°.

Left and right turns

A turn is always made relative to the way the person is currently facing, not relative to the page.

The row most people get wrong is "facing south". Someone walking south who turns left ends up walking east, which is to the right side of your page. If that feels odd, turn the question paper upside down for a second and it becomes obvious.

The drawing method

1. Put a small compass cross at the top of your rough work: N up, E right.
2. Mark the start with a dot and label it.
3. Draw each leg as a line with an arrow, writing the distance beside it.
4. After each turn, write the new heading at the corner (for example "now S").
5. For the final answer, join the start to the end point and read the direction of the end from the start.

For longer paths, keep a running total instead of a picture: east is +x, north is +y. Add each leg to the right coordinate. The end point's coordinates give both the distance and the direction.

Shortest distance

When the net movement is along both axes, the straight-line distance is the hypotenuse of a right-angled triangle: √(east–west gap² + north–south gap²).

The common Pythagorean triples cover almost every question: 3-4-5, 6-8-10, 5-12-13, 8-15-17, 9-12-15 and 7-24-25. If the numbers do not fit a triple, expect a surd such as 5√2 in the options.

Worked examples

Example 1. A person walks 5 km north, turns right and walks 3 km, then turns right again and walks 5 km. Where are they from the start?

• North 5: at (0, 5). Right from north is east. East 3: at (3, 5).
• Right from east is south. South 5: at (3, 0).
• The end point is 3 km east of the start.

Example 2. A person walks 6 km east and then 8 km north. How far are they from the start, and in which direction?

• The end point is (6, 8). Distance = √(36 + 64) = √100 = 10 km.
• Both east and north are positive, so the end point is north-east of the start.

Example 3. A cadet walks 4 km north, turns right and walks 6 km, turns right and walks 10 km, then turns left and walks 2 km. Find the distance and direction from the start.

• North 4: (0, 4). Right → east 6: (6, 4).
• Right from east → south 10: (6, −6).
• Left from south → east 2: (8, −6).
• Distance = √(64 + 36) = 10 km. East is positive and north is negative, so the cadet is south-east of the start.

Example 4 (turns in degrees). A person faces north. They turn 135° clockwise, then 90° anticlockwise, then 180°. Which way do they face?

• Net turn = +135 − 90 + 180 = 225° clockwise from north.
• 225° is south-west. (A 180° turn is the same either way, so its direction does not matter.)

Example 5 (relative position). P is 5 km north of Q. R is 5 km east of Q. Where is R with respect to P?

• Put Q at (0, 0). Then P is (0, 5) and R is (5, 0).
• From P to R: 5 east and 5 south. R is south-east of P, at a distance of 5√2 ≈ 7.07 km.

Shadow questions

These rest on one fact: the Sun rises in the east and sets in the west, and a shadow always points away from the Sun.

Questions are almost always set in the morning or evening. Noon is avoided because the direction of a noon shadow depends on latitude and season, and much of India lies close to the Tropic of Cancer.

Method: fix the shadow's compass direction from the time of day, then match it to the person's left, right, front or back.

Example 6. In the morning, a person's shadow falls to their right. Which way are they facing?

• Morning shadow points west. So west is on their right.
• A person with west on their right is facing south.

Example 7. In the evening, a person stands facing north. On which side does their shadow fall?

• Evening shadow points east. Facing north, east is on the right. The shadow falls to their right.

Practice set

1. A person walks 10 km south, turns left and walks 4 km. In which direction are they from the start?
2. A person walks 3 km west and then 4 km south. What is the shortest distance from the start?
3. Facing west, a person turns 90° clockwise twice. Which way do they face now?
4. A person walks 2 km east, turns left and walks 3 km, turns left and walks 6 km, then turns left and walks 3 km. How far and in which direction are they from the start?
5. In the evening, two friends stand facing each other. The first friend's shadow falls exactly to their left. Which direction does the second friend face?
6. Facing south-east, a person turns 270° anticlockwise. Which direction do they face now?
7. X is 12 km west of Y. Z is 5 km south of Y. How far is Z from X?

Answers:

1. South-east. Left from south is east, so the end point is (4, −10).
2. 5 km. √(9 + 16) = 5, towards the south-west.
3. East. West → north → east.
4. 4 km west. The path runs (2, 0) → (2, 3) → (−4, 3) → (−4, 0).
5. North. The evening shadow points east. East on your left means you face south, so the friend opposite faces north.
6. South-west. 135° − 270° = −135°, which is 225°. A 270° anticlockwise turn is the same as 90° clockwise.
7. 13 km. X is (−12, 0) and Z is (0, −5), so the distance is √(144 + 25) = √169 = 13.

What to do next

• Redo Examples 3 and 4 using coordinates only, without a drawing, and check you get the same answers.
• Do 10 direction questions a day for a week, timing each. Aim for under 45 seconds.
• Practise five shadow questions until the morning-west, evening-east rule is automatic.
• Move on to seating arrangement, which uses the same left-right discipline, and revisit blood relations for the draw-as-you-read habit.