Direction Sense for CUET General Aptitude

Q: How do you track a walk with coordinates?

Treat the start as (0, 0), with east as +x and north as +y. For each leg, first update the heading, then add the distance to the right total. At the end, (x, y) tells you everything.

Q: How do you name the direction of the end point from the start?

Look at the signs of the final (x, y). If one is zero, the answer is a main direction: (0, positive) is north. If both have the same size, it is an exact diagonal: (5, 5) is north-east. If the sizes differ, such as (5, 2), questions ask for the general direction, and (5, 2) counts as north-east.

Q: How do you solve relative position questions about places?

Put one place at (0, 0), usually the one mentioned most, and write every other place as coordinates from the clues. Then subtract coordinates to get the direction or distance between any two places.

About 10 min to learn · 67 questions

Direction sense questions describe a walk, a set of turns, a shadow or a few places on a map, and ask where someone ends up or which way they face. None needs a formula beyond Pythagoras. What they test is whether you keep track of the heading after every turn and read 'from' the right way round. This lesson covers the eight directions, left and right turns, net turns, tracking a walk with coordinates, straight-line distance, shadows, relative positions and coded directions.

Syllabus area: Logical and Analytical Reasoning

On this page · 8 sections

01The core idea
02Directions and turns
03Walks and distances
04Shadows and places
05Exam shortcuts
06Common mistakes
07Quick revision
08Check your understanding

The core idea

Every direction question is a walk to keep track of. Two habits settle almost all of them: turn from the direction you are facing, never from the page, and keep a running east–west total and north–south total instead of trying to picture the whole path.

At the end, those two totals give everything: the direction of the end point, its straight-line distance by Pythagoras, and the direction back. A ten-second sketch or a small table beats doing it in your head.

Directions and turns

What are the eight directions on a compass?

There are four main directions, north, east, south and west, and four in between: north-east, south-east, south-west and north-west. On paper north is up, east right, south down and west left. Going clockwise from north, each step is 45°.

Clockwise from north: N, NE, E, SE, S, SW, W, NW. Each step is 45°, so a right turn moves two steps.

Direction	Opposite
North	South
East	West
North-east	South-west
North-west	South-east

What does "turn left" or "turn right" mean for each facing direction?

A right turn is 90° clockwise and a left turn 90° anticlockwise, measured from the direction you face at that moment. So "left" points to a different compass direction depending on which way you face.

Facing	After a right turn	After a left turn	After an about-turn
North	East	West	South
East	South	North	West
South	West	East	North
West	North	South	East
North-east	South-east	North-west	South-west
South-west	North-west	South-east	North-east

Watch out

Facing south, your right hand points west and your left hand east, the reverse of the map. If in doubt, turn the paper so that the way you are walking points up, and read left and right off your own hands.

How do you find the final direction after several turns?

Turn every turn into degrees, clockwise as plus and anticlockwise as minus, add them, and make one turn from the starting direction. Right is +90°, left −90°, an about-turn 180°, and a full 360° changes nothing.

Example 1 · Net turn

Arjun faces west. He turns 45° clockwise, then 180°, then 90° anticlockwise. Which way does he face?

Net turn: $45 + 180 - 90 = 135^\circ$ clockwise.
Clockwise from west: north-west at 45°, north at 90°, north-east at 135°.

Answer

North-east

Exam shortcut

With left and right turns only, count lefts minus rights. Two net lefts is an about-turn, three net lefts equal one right, and four bring you back.

Walks and distances

How do you track a walk with coordinates?

Treat the start as $(0, 0)$ , with east as $+x$ and north as $+y$ . For each leg, first update the heading, then add the distance to the right total. At the end, $(x, y)$ tells you everything.

Example 2 · A four-leg walk

Manpreet walks 10 km north, turns right and walks 9 km, turns right and walks 2 km, then turns left and walks 6 km. Where does she end, and how far is she from the start?

North 10: $(0, 10)$ . Right, so east 9: $(9, 10)$ .
Right, so south 2: $(9, 8)$ . Left from south is east, 6: $(15, 8)$ .
Distance: $\sqrt{15^2 + 8^2} = \sqrt{289} = 17$ km.

Answer

15 km east and 8 km north of the start, 17 km away

Manpreet's walk on a grid: 10 km up from A, 9 km right, 2 km down, 6 km right to B. A dashed line joins A to B and is marked 17. — The path walked is 27 km. The straight line from A to B is 17 km, by the 8-15-17 triple.

Exam shortcut

Writing each leg's heading before adding any distance is the one habit that prevents most errors. The small table takes twenty seconds, and you cannot lose a turn in it.

How do you find the straight-line distance from the starting point?

Net the east–west legs into one number and the north–south legs into another, then use Pythagoras. Opposite legs subtract, legs at right angles combine through Pythagoras, and legs in the same direction add.

Legs	Distance	Multiples
3 and 4	5	6 and 8 give 10; 9 and 12 give 15
5 and 12	13	10 and 24 give 26
8 and 15	17	16 and 30 give 34
7 and 24	25
$k$ and $k$	$k\sqrt{2}$	5 and 5 give $5\sqrt{2}$

Example 3 · Netting the legs

A tractor goes 7 km south, turns left and goes 12 km, turns left and goes 12 km. How far is it from the start?

Left from south is east: 12 km east. Left from east is north: 12 km north.
North–south: 7 south and 12 north, net 5 km north. East–west: 12 km east.
Distance: $\sqrt{12^2 + 5^2} = 13$ km.

Answer

13 km

Watch out

The total distance walked, 31 km here, is a different quantity and almost always a wrong option. And a leg can overshoot the start: 3 km east then 8 km west leaves you 5 km west, not east.

How do you name the direction of the end point from the start?

Look at the signs of the final $(x, y)$ . If one is zero, the answer is a main direction: $(0, \text{positive})$ is north. If both have the same size, it is an exact diagonal: $(5, 5)$ is north-east. If the sizes differ, such as $(5, 2)$ , questions ask for the general direction, and $(5, 2)$ counts as north-east.

Watch out

"Where is the start from the end?" is the opposite of "where is the end from the start?". If you are 6 km north of home, home is 6 km south of you. A diagonal leg of $k\sqrt{2}$ km north-east moves you $k$ km east and $k$ km north; split it and carry on.

Shadows and places

How do shadows tell you the direction?

A shadow always points away from the sun. In the morning after sunrise the sun is in the east, so shadows fall west; in the evening before sunset the sun is in the west, so shadows fall east.

Person faces	Morning shadow, west, is	Evening shadow, east, is
North	To the left	To the right
East	Behind	In front
South	To the right	To the left
West	In front	Behind

Example 4 · A shadow on the left

In the evening before sunset, Priyanka's shadow falls exactly to her left. Which way is she facing?

An evening shadow points east, so east is on her left.
East is on your left when you face south.

Answer

South

How do you solve relative position questions about places?

Put one place at $(0, 0)$ , usually the one mentioned most, and write every other place as coordinates from the clues. Then subtract coordinates to get the direction or distance between any two places.

Example 5 · Places on a map

The hospital is 9 km west of the college. The stadium is 12 km south of the college. The mall is 9 km west of the stadium. Where is the mall from the hospital?

College $(0, 0)$ , hospital $(-9, 0)$ , stadium $(0, -12)$ , mall $(-9, -12)$ .
Mall minus hospital: $(0, -12)$ .

Answer

12 km south of the hospital

Watch out

"P is 4 km north of Q" means P = Q + $(0, 4)$ , which puts Q south of P. Many wrong answers read it the other way round.

How do you handle coded directions like "north is called east"?

Treat the code as a rotation of the compass, occasionally a mirror. Work out how far the example turns a real direction, check it on a second pair if one is given, and apply the same turn. To decode, turn the other way.

"North is called east, east is called south…" is a 90° clockwise rotation, so north-west is called north-east.
"South-east is called north" is a 135° anticlockwise rotation.
"East and west swap, north and south stay" is a mirror: only the east–west part changes, so south-east becomes south-west.

Example 6 · Decoding

In a code, every direction is named after the direction 90° clockwise from it. A note says the bank is "north" of the park. What is the real direction?

Coded name = real direction turned 90° clockwise.
Undo it: turn "north" 90° anticlockwise, which gives west.

Answer

West

Check: real west turned 90° clockwise is north.

Exam shortcuts

Turn from your heading. Never from the page.
Two running totals. East–west and north–south, updated leg by leg.
Triples. 3-4-5, 5-12-13, 8-15-17, 7-24-25 make the root instant.
Shadows. Morning west, evening east.
Codes. Find the rotation, check it on a second pair, reverse it to decode.

Common mistakes

Forgetting that a turn changes what "left" means.
Measuring from the end instead of the start.
Reading "A is north of B" backwards.
Giving the total distance walked.
Adding two legs instead of using Pythagoras. 6 east and 8 north is 10 away, not 14.
Missing that a leg overshoots the start.
The wrong shadow rule.
Calling $(5, 2)$ exactly north-east. Exact diagonals need equal legs.
Applying a code the wrong way. Check by applying it back.

Quick revision

Directions

Clockwise: N, NE, E, SE, S, SW, W, NW, 45° apart
Right +90°, left −90°, about-turn 180°
Facing south: right is west, left is east

Walks

Start $(0, 0)$ , east $+x$ , north $+y$
Heading first, then distance
Distance $= \sqrt{x^2 + y^2}$

Shadows and codes

Morning shadow west, evening shadow east
Code = rotation or mirror. Decode by turning back

Right triangles and Pythagoras are worked in lines, triangles and circles, and rules that run one way in coding-decoding.

Next · 07Quick revision

Check your understanding

67 questions, grouped by type, easy to hard. Pick an answer and check it. The worked solution opens when you ask for it.

Distance and final positionQ1 of 67Q1

Distance and final position

20 questions

Check your understanding

Distance and final position

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Turns and facing

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Shadows and the sun

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Relative positions of places

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