Direction Sense questions with answers and concepts

Learn direction sense with concept notes and worked examples, then practise focused questions with explained answers. Build accuracy for placement and competitive aptitude tests before trying timed mode.

123 practice questionsPage updated 24 Sept 2026Review metadata pendingPractice questions

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Direction Sense tests your ability to navigate using cardinal directions (North, South, East, West) and their intercardinal directions (NE, NW, SE, SW). These problems involve tracking movement, calculating final positions, determining distances from starting points, and understanding left/right turns based on facing direction. Mastery of direction sense is essential for solving complex logical puzzles involving spatial reasoning.

Key formulas and rules

9 rules

Pythagorean Displacement: $D = (Δ x)^{2} + (Δ y)^{2} = (x_{east} - x_{west})^{2} + (y_{north} - y_{south})^{2}$

Clockwise Cardinal Cycle ( $9 0^{\circ}$ Right): $North + 9 0^{\circ} East + 9 0^{\circ} South + 9 0^{\circ} West + 9 0^{\circ} North$

Anticlockwise Cycle ( $9 0^{\circ}$ Left): $North - 9 0^{\circ} West - 9 0^{\circ} South - 9 0^{\circ} East - 9 0^{\circ} North$

Relative Orientations When Facing North: $Left = West$ , $Right = East$ , $Back = South$

Relative Orientations When Facing South: $Left = East$ , $Right = West$ , $Back = North$

Relative Orientations When Facing East: $Left = North$ , $Right = South$ , $Back = West$

Relative Orientations When Facing West: $Left = South$ , $Right = North$ , $Back = East$

Solar Shadow Vector: $v_{shadow} = - v_{sun}$ (at sunrise $v_{sun} = East ⟹ shadow points West$ ; at sunset $shadow points East$ )

Noon Shadow Geometry: In northern temperate zone, sun is due South at solar noon $⟹$ shadows point due North

Key concepts

Cardinal and Intercardinal Directions

The four cardinal directions are North (N), South (S), East (E), and West (W). The intercardinal directions are Northeast (NE), Northwest (NW), Southeast (SE), and Southwest (SW). North, South, East, and West are absolute fixed directions in space. In contrast, egocentric directions (left, right, ahead, behind) are relative to a person's current facing orientation.

Left and Right Turns

Left and right depend on which direction you are facing. If facing North: left is West, right is East. If facing South: left is East, right is West. If facing East: left is North, right is South. If facing West: left is South, right is North. A useful mnemonic: after turning right, you face the next direction clockwise; after turning left, you face the next direction anticlockwise. Always track your current facing direction after each turn.

Calculating Final Position

To find final position from a series of movements: (1) Start at origin (0,0) facing the given initial direction, (2) Assign coordinates: North (+y), South (-y), East (+x), West (-x), (3) Add/subtract distances based on movements, (4) Final coordinates show displacement from start. For diagonal movements (NE, NW, SE, SW), both x and y change by the same amount. Example: Moving 10m NE means +10/sqrt2 in both x and y (approximately 7.07m each).

Distance from Starting Point

The shortest distance from starting point uses the Pythagorean theorem: distance = $x^{2} + y^{2}$ , where x is total East-West displacement and y is total North-South displacement. If final position is (a,b), distance = $a^{2} + b^{2}$ . Direction from start to finish is determined by the signs of x and y: (+,+)=NE, (-,+)=NW, (-,-)=SW, (+,-)=SE. This assumes standard Cartesian coordinates with East as positive x and North as positive y.

Shadow and Sun Position Problems

Shadow problems connect time of day with direction. In the Northern hemisphere: (1) Sunrise (morning): Sun in East, shadow towards West, (2) Noon: Sun overhead (South in tropics, varying by latitude), shadow minimal or towards North, (3) Sunset (evening): Sun in West, shadow towards East. A person's shadow indicates the opposite direction of the sun. If someone faces the direction of their shadow at morning, they face West.

Complex Movement Patterns

For multi-step problems: Track current position (x,y) and current facing direction separately. After each movement segment, update position. After each turn, update facing direction without changing position. Common patterns include: rectangular paths (return to start), spiral paths, backtracking, and figure-eight patterns. For 'return to start' problems, the sum of all North-South movements must equal zero, and sum of all East-West movements must equal zero.

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Worked examples

Example 1

A person walks 3 km North, then turns East and walks 4 km. How far is he from his starting point and in which direction?

Solution

Step 1: Formulate displacement vectors.

Δ y = + 3 km (North), Δ x = + 4 km (East)

Step 2: Apply Pythagoras theorem.

d = (Δ x)^{2} + (Δ y)^{2} = 4^{2} + 3^{2} = 16 + 9 = 25 = 5 km

Step 3: Determine direction.
Both $Δ x > 0$ and $Δ y > 0 ⟹$ North-East.

Answer: 5 km North-East.

Example 2

Rohan walks 10 m South, turns left and walks 12 m, then turns left again and walks 16 m. Finally, he turns left and walks 4 m. Find his shortest direct distance from the starting point.

Solution

Step 1: Track coordinates taking origin $(0, 0)$ as start.
- South 10 m: $(0, - 10)$
- Left turn (East) 12 m: $(12, - 10)$
- Left turn (North) 16 m: $(12, - 10 + 16) = (12, 6)$
- Left turn (West) 4 m: $(12 - 4, 6) = (8, 6)$

Step 2: Compute shortest distance.

d = 8^{2} + 6^{2} = 64 + 36 = 100 = 10 m

Answer: 10 metres.

Example 3

A man faces North. He turns 135° clockwise, then 180° anticlockwise, and finally 90° clockwise. Which direction is he facing now?

Solution

Step 1: Net angular rotation calculation.

Net Rotation = + 13 5^{\circ} - 18 0^{\circ} + 9 0^{\circ} = + 4 5^{\circ} (clockwise)

Step 2: Apply rotation from North.

North + 4 5^{\circ} clockwise = North-East

Answer: North-East.

Example 4

At sunrise, two friends A and B stand face-to-face in an open field. If A's shadow falls directly to the right of B, which direction is A facing?

Solution

Step 1: Establish shadow orientation at sunrise.
At sunrise, the sun is in the East, so all shadows project towards the West.

Step 2: Determine B's orientation.
A's shadow falls to B's right $⟹$ B's right side points West. A person facing South has West on their right (whereas facing North has East on their right). Therefore, B faces South.

Step 3: Determine A's facing direction.
Since A and B stand face-to-face, A faces the opposite direction of B. Because B faces South, A must face North.

Answer: North.

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

Rohit starts from point A and walks 5 km towards East. Then he turns to his right and walks 3 km. Then he turns to his left and walks 4 km. How far and in which direction is he from point A?

9.49 km, South-East
8 km, East
7 km, North
8 km, North-East

Answer: A. 9.49 km, South-East

Explanation

The final position is (9,-3), so the distance is √(9²+3²) = √90 ≈ 9.49 km, in the South-East direction.

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

One morning, Rita started walking towards the Sun. After walking some distance, she turned to her left and continued walking. Then she turned to her right, walked for some distance and again turned to her right. In which direction is she facing now?

North
South
East
West

Answer: B. South

Explanation

Step 1: In the morning, walking towards the Sun means walking East.
Step 2: Turning to her left puts Rita facing North.
Step 3: Turning to her right from North puts her facing East.
Step 4: Turning to her right again from East puts her facing South.
Therefore, she is facing South.

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

A man is facing North-West. He turns 90 deg in the clockwise direction, then 180 deg in the anticlockwise direction. Which direction is he facing now?

North-East
South-West
North-West
South-East

Answer: B. South-West

Explanation

Step 1: Initial direction = North-West.
Step 2: 90 deg clockwise from North-West = North-East.
Step 3: 180 deg anticlockwise from North-East = South-West.
Answer: South-West

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Always draw a rough diagram with coordinate axes - visual representation prevents errors in complex multi-turn problems.
Use the clock-wise rule: N->E->S->W->N for right turns, and reverse for left turns. This is faster than memorizing all combinations.
For distance calculation, only consider net displacement (final minus initial), not total distance walked.
In shadow problems, remember: Shadow direction = Opposite of Sun direction. Morning = East sun = West shadow.
When turning 'back' or 180 deg, you're simply facing the opposite direction - no need to overthink left/right.
For 'return to starting point' verification: sum of all North movements must equal sum of all South movements, and East equals West.
If a person faces the direction of their own shadow at evening time, they face East (shadow is East at sunset).

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