Logical Reasoning · Lesson 05

Crack Direction Sense
one arrow at a time.

Direction sense is just walking a path on a grid — turns, distances, and the straight line back to start. Draw it, and the answer is right there.

Learning time

18 min · self-paced

Exam weight

2–3 questions / set

Sections

9 modules

Start learning Skim the cheat sheet

Topic map

9 sections, built in the order they actually click.

From "which way is North-East" to "find the shortest distance and final bearing in under 60 seconds."

Topic 01

The 8 directions

North, the diagonals, and how a compass is laid out.

Topic 02

Left & right turns

Turns are relative to where you face — not the page.

Topic 03

Clockwise logic

Degrees, clockwise vs anticlockwise rotation.

Topic 04

Path tracing

Convert a story of moves into a drawn route.

Topic 05

Shortest distance

The Pythagoras / 3-4-5 displacement shortcut.

Topic 06

Final direction

Which way is point B from point A at the end.

Topic 07

Shadows & sun

Sunrise / sunset shadow-direction questions.

Topic 08

Common tricks

High-frequency examiner setups and how they fool you.

Topic 09

Mastery check

Mini test + revision summary to lock it in.

Foundation · 01

Four building blocks. Everything else is just walking.

Get these four reflexes automatic and the actual questions become bookkeeping. Tap to explore each.

Interactive

The 8-point compass

North is always up. The 4 cardinals (N, E, S, W) sit at 90° apart; the 4 ordinals (NE, SE, SW, NW) bisect them at the diagonals. Tap any point on the compass.

✓ Remember

Clockwise from North: N → E → S → W. The word "NEWS" is the order.

✗ Don't mix

North-East means "between N and E" — written N first, never "EN".

Try it yourself

Walk the path and track the displacement.

Set the starting direction, walk two legs, and let the grid show both the route and the straight-line answer back to the start.

Start facing

Walk3 km

Then turn

Walk again4 km

Facing North, walk 3 km, turn left to West, then walk 4 km. You finish 5 km from the start, toward the North-West.

The dashed line is the shortest distance back to start, which is the quantity these questions usually ask for.

Method · 02

The 4-step routine that never fails on a path question.

Draw first, calculate last. The mistake is always trying to track position in your head.

STEP 1

Fix start & facing

Plant a dot for the start. Note the initial facing direction (usually North if unstated).

STEP 2

Draw every move

Walk one segment per instruction. Keep N up. Use rough lengths — proportion matters more than precision.

STEP 3

Resolve turns live

For each turn, rotate from your CURRENT facing. Re-orient before drawing the next segment.

STEP 4

Read off the answer

Connect start → end. Net direction is the bearing; net distance uses Pythagoras on the X/Y gaps.

Pro tip. Net displacement only depends on the start and end points. All the wiggles in between cancel — so once you know the final X and Y offset, distance is just √(X² + Y²).

Question types · 03

The 6 formats every exam recycles.

Name the format in the first 5 seconds and your hand already knows what to draw.

Final position & distance

Type 01 · ~50 sec target

What it looks like

A walks 4 km N, then 3 km E. How far is A from start, and in which direction?

How to identify

A clean sequence of cardinal moves, ending with "how far / which direction from start".

How to solve

Trace the path, find net X (E–W) and net Y (N–S), then distance = √(X²+Y²). The default and most common type.

Mini example. 4 km N + 3 km E → net (3 E, 4 N) → distance 5 km, direction NE of start.

Trap: Adding all distances (4+3=7) instead of finding net displacement (5). Distance ≠ total walked.

Turn-based (left / right)

Type 02 · ~70 sec target

What it looks like

Facing instructions like "turn left, walk 2 km, turn right…" without stating absolute directions.

How to identify

You're told turns, not compass directions. You must track facing yourself at each step.

How to solve

Maintain a "current facing" variable. Apply each left/right relative to it, THEN walk. Re-orient every turn.

Mini example. Face N, walk 3. Turn right (→E), walk 4. Turn right (→S), walk 3. End: 4 km E of start.

Trap: Applying left/right relative to North every time instead of your current facing.

Shortest-distance (Pythagoras)

Type 03 · ~60 sec target

What it looks like

Asks specifically for the shortest / straight-line distance between two points.

How to identify

Keyword "shortest distance" or "how far directly". Almost always a 3-4-5 or 5-12-13 triangle.

How to solve

Find the right-angled triangle formed by net horizontal and vertical legs. Apply √(a²+b²).

Mini example. Net 6 E and 8 N → shortest distance = √(36+64) = √100 = 10 km.

Trap: Forgetting that opposite moves cancel before you apply Pythagoras. Net the legs first.

Final direction / bearing

Type 04 · ~55 sec target

What it looks like

"In which direction is B from A?" or "A is in which direction from the start point?"

How to identify

The answer is one of the 8 directions, not a distance.

How to solve

Compare end vs start: positive net N & E → NE; net N & W → NW, etc. Diagonal if both axes move.

Mini example. End is 3 km E and 3 km S of start → B is to the South-East of A.

Trap: Reversing the reference: "B from A" is the opposite arrow of "A from B".

Shadow / sun direction

Type 05 · ~40 sec target

What it looks like

Mentions a time of day, the sun, and a person/pole casting a shadow.

How to identify

Watch for "early morning", "sunset", "shadow fell to his left", etc.

How to solve

Sun East in morning, West in evening. Shadow is opposite the sun. Use the shadow to fix the person's facing.

Mini example. Morning, shadow falls to a man's right → sun (East) is to his left → he faces North.

Trap: Forgetting shadow is opposite the sun, not toward it.

Degree-rotation

Type 06 · ~50 sec target

What it looks like

Movements given as "rotate 135° clockwise" rather than left/right.

How to identify

Angles in degrees (45, 90, 135, 180, 270). Often combined with a starting direction.

How to solve

Convert: every 45° = one compass point clockwise. Count points from the start direction.

Mini example. Facing N, rotate 135° clockwise → N→NE→E→SE → ends facing South-East.

Trap: Mixing clockwise and anticlockwise, or forgetting 45° steps land on diagonals.

Worked examples · 04

Watch three routes solved arrow by arrow.

Same method, rising difficulty. Step through manually — or replay the path animation.

Problem

QuestionA man walks 4 km towards North, then turns right and walks 3 km. How far is he from the starting point, and in which direction?

Net East

—

Net North

—

Distance

—

Trace the route

Step 1. Plant the start. He faces North to begin.

1 / 4

Common traps · 05

The 6 mistakes that quietly cost marks.

Each one shows up in nearly every paper, dressed slightly differently. Spot the pattern.

Trap 01 · Distance ≠ total walked

4 km N + 3 km E = 7 km away

Shortest distance is the straight line: √(4²+3²) = 5 km. Add legs only for "total distance travelled".

Trap 02 · Left/right is relative

"Turn left" always means turn West

Left depends on your current facing. Facing South, your left is East, not West.

Trap 03 · Shadow is opposite the sun

Morning shadow points East (toward sun)

Sun rises East → shadows fall West. The shadow always points away from the sun.

Trap 04 · "From A" vs "from B"

B is NE of A, so A is NE of B

Reverse the arrow. If B is NE of A, then A is SW of B — the exact opposite.

Trap 05 · Diagonal ≠ cardinal

Net 3 E and 3 N → "East"

Equal movement on both axes is a diagonal. 3 E + 3 N → North-East, not East.

Trap 06 · Forgetting to cancel

Applying Pythagoras to raw legs

Net opposite moves first (E−W, N−S). Then apply √ on the remainders, never the originals.

Tips & tricks · 06

Six tactical moves used by fast solvers.

Small habit-level shifts you can apply on your very next practice set.

TIP 01

Always keep North up

Orient your scribble with N at top, every time. Consistency kills careless errors.

TIP 02

Track facing as an arrow

For turn-based questions, draw a tiny arrow for your current facing and rotate it at each turn.

TIP 03

Memorise 3-4-5 & 5-12-13

Most "shortest distance" answers are these Pythagorean triples. Recognise them instantly.

TIP 04

Net the axes separately

Sum all East/West into one number, all North/South into another. Then combine.

TIP 05

Right = clockwise

Right turn = clockwise (N→E→S→W). Left = anticlockwise. Lock this reflex in.

TIP 06

Sun: East-morning, West-evening

Shadow opposite the sun. This single rule answers every shadow question.

Mini practice · 07

Try it on 4 questions — instant feedback included.

Mixed difficulty, no timer pressure. An explanation (and a diagram) for every answer.

Question 1 of 4Easy

Score · 0/4

A walks 6 km East, then 8 km North. How far is he from the start?

Streak target: 3 in a row.

Revision · 08

One-page cheat sheet for the last 5 minutes.

Print it, screenshot it, or glance at it before your slot.

Turns & rotation

Action	Effect	N becomes
Turn right	+90° clockwise	East
Turn left	−90° anticlockwise	West
About-turn	180°	South
45° clockwise	half a turn-point	North-East

Distance & direction

Shortest distance	√(netX² + netY²)
Triples to know	3-4-5 · 5-12-13 · 8-15-17
Net X	Σ East − Σ West
Net Y	Σ North − Σ South
Both axes move	diagonal (NE/NW/SE/SW)

Last-minute reminders

01Keep North up. Draw — never track in your head.
02Turns are relative to your current facing.
03Distance walked ≠ displacement from start.
04Cancel opposite moves before Pythagoras.
05Right = clockwise, Left = anticlockwise.
06Sun East at dawn, West at dusk; shadow is opposite.
07"B from A" is the reverse arrow of "A from B".
08Equal X and Y movement → a diagonal direction.

What's next · 09

Lesson done. Time to lock it in.

Practice the hard stuff, queue the next topic, or revisit what tripped you up.

Practice 20 direction questions

Adaptive difficulty, instant explanations, mistakes auto-added to your notebook. ~16 minutes.

Start practice

Continue to next topic

Up next: Blood relations. Another mapping-on-paper skill.

Continue

Revisit mistakes

Review the turn-based and shadow questions — the two highest-error types.

Open notebook