ExamShortcut
🔍Log in

Direction & Distance

🔒 Log in to track
medium importance~1-2 Q in Tier 18 formulas⚡ 6 shortcuts4 subtopics
OverviewLearn (4)Formulas (8)Examples (4)Practice (53)
All subtopics·Subtopic 2 of 4

Direction faced and net direction

🔒 Log in to track
⏱ 5 min read🧩 5 question types🎯 14 practice Q
The idea in one minute

Two kinds of question live here. One asks which way a person faces after some turns. The other asks in which direction the end point lies from the start. Write the direction after every turn, and never trust your memory over three turns.

01

Which way is he facing now

Only the turns matter here. The distances are decoration.

A right turn of 90 degrees moves you one step clockwise on this circle: North, East, South, West, and back to North. A left turn moves one step the other way.

Start facingAfter a right turnAfter a left turn
NorthEastWest
EastSouthNorth
SouthWestEast
WestNorthSouth

Rule: Right is one step clockwise. Left is one step back. An about-turn (180 degrees) is two steps.

02

Count the quarter-turns

One quarter-turn is 90 degrees. Count rights as plus and lefts as minus. Add them.

Example: facing West, a man turns 90 degrees anticlockwise, then 270 degrees clockwise. That is −1+3=+2-1 + 3 = +2 quarter-turns. Two steps clockwise from West is East.

Four quarter-turns bring you back to where you started. So cross out 4 whenever it appears.

Tip: 270 degrees clockwise is the same as 90 degrees anticlockwise. Both end in the same place.

03

Which direction is the end point

Now the path matters and the facing does not. Find the net East move and the net North move. Then read the compass from their signs.

East moveNorth moveDirection
plusplusNorth-East
minusplusNorth-West
plusminusSouth-East
minusminusSouth-West

If one move is zero, use one word only. A net move of 4 km North and 0 East is simply North.

"Direction of B from A" means: stand at A, look at B. Swap the two people and the answer flips. North-East becomes South-West.

04

Turns in the middle of a walk

"Walks 5 km, turns left, walks 3 km." The word "left" depends on the way he walks now. So track the direction leg by leg.

Example: a man walks North, turns right and walks 4 km, then turns left and walks 3 km. Right of North is East. Left of East is North. He moves 4 km East and 3 km North. He ends North-East of the start.

05

Turning back

"Turns back", "returns" and "about-turn" all mean 180 degrees. He now faces the opposite way.

A man walks 6 km East, then turns back and walks 2 km. He faces West. He is 6−2=46 - 2 = 4 km East of the start.

Watch: The end direction and the facing direction are two different answers. Read which one the question wants.

06

Questions that ask both

A hard question gives turns and then asks the direction of the end point. Keep two lists.

  1. List one: the direction he faces after each turn.
  2. List two: the net East and North moves.

Do not read one list from the other. A quick picture check helps. If he ended North and East of the start, he cannot be South-West.

07

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common3 practice Q

Net quarter-turns for the final facing

How to spot it:

A starting direction and a list of turns are given. The question asks which way he faces now.

Method

  1. Count a right turn as +1, a left turn as -1 and an about-turn as 2.

  2. Add them up and drop any 4.

  3. Move that many steps clockwise from the start.

Why it works:

Each turn is a quarter of a full circle, and four quarters bring you home.

Try this

A man faces South. He turns 90 degrees clockwise, then 180 degrees, then 90 degrees anticlockwise. Which way does he face now?

Show solution

  1. Turns: +1, +2, -1.

  2. Total: +2.

  3. Two steps clockwise from South: West, then North.

Answer

North

Type 2very common2 practice Q

Direction of the end point from the start

How to spot it:

A path is given. The question asks in which direction the finish is from the starting point.

Method

  1. Find the net East-West move and the net North-South move.

  2. Look at the sign of each.

  3. Join the two words. Use one word if a move is zero.

Why it works:

The direction of the end point is the compass word of the net move.

Try this

Priya walks 6 km North, 2 km East, 9 km South and then 2 km East. In which direction is she from the starting point?

Show solution

  1. East-West: 2 + 2 = 4 km East.

  2. North-South: 6 - 9 = 3 km South.

  3. East and South make South-East.

Answer

South-East

Type 3common2 practice Q

Left and right turns in the middle

How to spot it:

The path has turns such as "turns left" or "turns right", and the final direction is asked.

Method

  1. Write the direction he faces at the start.

  2. After each turn, write the new direction. Overwrite the old letter.

  3. The last letter is the final direction.

Why it works:

The words left and right change meaning with every turn, so only a written chain is safe.

Try this

Walking East, Arun turns right, walks 4 km, and then turns right again. Which way does he face now?

Show solution

  1. Start: East.

  2. Right turn: South.

  3. Right turn again: West.

Answer

West

Type 4common2 practice Q

Turning back and returning

How to spot it:

The path says "turns back", "returns" or "retraces" in the middle.

Method

  1. An about-turn makes him face the opposite direction.

  2. A new leg after it cancels part of the old one.

  3. Finish the rest of the path and find the net moves.

Why it works:

Turning back sends him along the same line the other way, so the new leg reduces the gap.

Try this

A man walks 8 km North, turns back and walks 4 km, and then turns left and walks 3 km. How far and in which direction is he from the start?

Show solution

  1. Turning back: he faces South and walks 4 km. North-South: 8 - 4 = 4 km North.

  2. Left of South is East. He walks 3 km East.

  3. Net moves 3 East and 4 North give 5 km, towards North-East.

Answer

5 km, North-East

Type 5occasional

Facing and end point together

How to spot it:

A path with several turns is given. It asks for the distance and direction from the start.

Method

  1. Track the facing after each turn in list one.

  2. Turn each leg into a North, South, East or West move.

  3. Find the net moves, then the distance and the compass word.

Why it works:

The turns give the direction of each leg. The legs then give the net move.

Try this

Deepa faces West and walks 4 km. She turns right and walks 3 km, and then turns right again and walks 4 km. How far and in which direction is she from the start?

Show solution

  1. West 4 km, then right turn: North 3 km, then right turn: East 4 km.

  2. East-West: 4 West and 4 East cancel.

  3. Only 3 km North is left.

Answer

3 km, North

08

Formula sheet

Clockwise cycle
N→E→S→W→NN \to E \to S \to W \to N

Every right turn moves one step along this circle.

Anticlockwise cycle
N→W→S→E→NN \to W \to S \to E \to N

Every left turn moves one step along this circle.

Reading the end point
(x>0, y>0)⇒North-East(x>0,\ y>0) \Rightarrow \text{North-East}

x is the net East move and y is the net North move. Their signs give the compass word.

09

Shortcuts that save time

⚡ Write the direction after every turn

After each turn, write one letter: N, E, S or W. Overwrite the old letter. Three written letters are safer than one long chain in your head.

Example

Facing West, a man turns 90 degrees clockwise and then 180 degrees anticlockwise. Which way does he face?

Show solution

  1. West, then 90 clockwise: North.

  2. 180 either way: South.

Answer

South

⚡ Reverse the pair, flip the word

If B is North-East of A, then A is South-West of B. The mixed words flip together.

Example

B is 3 km East and 4 km North of A. In which direction is A from B?

Show solution

  1. B from A is North-East.

  2. Reverse the pair: A from B is South-West.

Answer

South-West

10

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Using 'left = West' without checking which way he faces.

Check the table of turns. Left of South is East.

Mistake 02

Counting an about-turn as one quarter-turn.

An about-turn is two quarter-turns, 180 degrees.

Mistake 03

Giving the facing when the question asks the direction from the start.

Underline the last line. 'Facing' and 'direction from the start' are different answers.

Mistake 04

Reading the end direction from the distances instead of the net moves.

Use the signs of the net East and North moves.

Mistake 05

Forgetting to flip the answer when the pair is reversed.

North-East becomes South-West when the two people swap places.

11

Quick revision

Read this the night before the exam.

  • Right turn: one step clockwise on N, E, S, W. Left turn: one step back.

  • An about-turn is two steps. Four quarter-turns are a full circle.

  • Net quarter-turns = rights minus lefts.

  • Direction of the end point: signs of the net East and North moves.

  • 'B from A' means stand at A and look at B. Reversing the pair flips the word.

  • Track the facing leg by leg when turns come in the middle.

  • Facing and end direction are two different answers.

12

Practice: 14 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 10 questions

Suggested time 7 min · wrong answers go to your mistake notebook automatically.

Continue learning