Quantitative Aptitude · Direction Tests

Relative Position and Direction Between Two Points

Updated 1 October 2026 · Fact-checked

Relative direction asks where a final point lies with respect to a starting point after a series of moves. Draw the path on a grid, add up the net north-south and east-west movement, then read the direction of the start-to-end line, with the start as reference.

Understand Relative Position and Direction Between Two Points

A direction question gives you a person who walks in steps: so far north, then east, then south, and so on. At the end you are asked in which direction the person is from the starting point, or the starting point from the person.

The four cardinal directions are North, East, South and West. The in-between ones are North-East (NE), North-West (NW), South-East (SE) and South-West (SW). Unless the question says otherwise, North is up on your paper and East is to the right.

The key idea is net displacement. Moves north and south cancel each other along the vertical line. Moves east and west cancel along the horizontal line. What remains is a net vertical shift and a net horizontal shift. Together they tell you the final direction.

The word with respect to decides the reference point. If the question asks the direction of A from B, stand at B and look at A. Reversing the question reverses the answer: if A is NE of B, then B is SW of A.

Key formulas to remember

Net north-south shift: Net N-S = (total North) − (total South); Positive means the end point is north of the start. Negative means south. Zero means no vertical shift.
Net east-west shift: Net E-W = (total East) − (total West); Positive means east of the start. Negative means west. Zero means no horizontal shift.
Reading the final direction: Net N and Net E → NE; Net N and Net W → NW; Net S and Net E → SE; Net S and Net W → SW; If one net shift is zero, the direction is a pure cardinal one: N, S, E or W.
Opposite directions: N ↔ S, E ↔ W, NE ↔ SW, NW ↔ SE; Use this when the question asks for the start from the end point instead of the end from the start.
Straight-line distance: Distance = √[(Net N-S)² + (Net E-W)²]; Needed when the question also asks how far the end point is from the start.

How to solve Relative Position and Direction Between Two Points questions

Use this method for any relative direction question. Always draw. Do not trust your head for more than two moves.

1Read the last line of the question first. Note which point is the reference (the one after 'from' or 'with respect to').
2Mark the start point on rough paper and draw a small compass with North at the top.
3Draw each move as an arrow in order. Write the distance on it. Where the person turns left or right, work out the new heading from the current one.
4Add all North moves and subtract South moves to get the net N-S shift. Do the same for East and West.
5Combine the two net shifts to get the direction of the end point from the start.
6If the question asks for the start from the end point, reverse the direction (N becomes S, NE becomes SW, and so on).
7Check your answer against the options. Confirm that it matches the reference point in the question.

Quickest way: Coordinate tally method

When to use it: Use it when there are three or more moves and the turns are clear. It is faster than a neat diagram under time pressure.

Treat the start as (0, 0). East is +x, West is −x, North is +y, South is −y.
After each move, write the change in x or y on the side. Do not redraw the whole path.
Add the x values and the y values separately.
Read the signs: (+, +) is NE, (−, +) is NW, (+, −) is SE, (−, −) is SW. A zero gives a pure direction.
Reverse the signs if the question asks for the start from the end.
Eliminate options that have the wrong sign on either axis. Often only one option is left.

Common mistakes in Relative Position and Direction Between Two Points

Giving the direction of the start from the end when asked the end from the start.
Students stop at the first direction they find and do not recheck the reference point.
Fix: Underline the reference point in the question. Stand at that point in your sketch and look toward the other.
Mixing up left and right turns.
Left and right depend on the way the person is currently facing, not on the page.
Fix: Facing North, right is East and left is West. Facing East, right is South. Turn clockwise for right, anticlockwise for left.
Adding opposite moves instead of cancelling them.
Students add all distances without thinking about direction.
Fix: Keep North and South in one tally and East and West in another. Subtract within each pair.
Calling a point NE when one net shift is zero.
Students see moves in both axes and assume the result has both.
Fix: Always compute the net values. If East and West cancel fully, the end point is directly North or South.
Drawing the path to the wrong scale and misjudging the final direction.
Rough sketches make a small shift look large, or the reverse.
Fix: Decide the direction from the net numbers, not from how the sketch looks.

Worked examples

Example 1

Ravi walks 6 km North, then 4 km East, then 2 km South. In which direction is he from his starting point? (A) North-East (B) South-East (C) North (D) East

Show the solution

Start at (0, 0). North 6 gives y = 6.
East 4 gives x = 4.
South 2 gives y = 6 − 2 = 4.
Net position is x = +4 and y = +4, so he is east and north of the start.
Both shifts are positive, so the direction is North-East.

Answer: (A) North-East

Example 2

Meera starts from a point and walks 10 m West, then turns right and walks 5 m, then turns right and walks 10 m. In which direction is she from the starting point? (A) North (B) South (C) East (D) West

Show the solution

Walking West, a right turn points North. So the 5 m move is North.
Facing North, a right turn points East. So the 10 m move is East.
Net East-West: 10 m West then 10 m East gives 0.
Net North-South: 5 m North.
Only a north shift remains, so she is directly North of the start.

Answer: (A) North

Example 3

A walks 8 km East, then 3 km North, then 11 km West, then 3 km South. In which direction is the starting point from A's final position? (A) East (B) West (C) North (D) South-East

Show the solution

Net East-West: 8 East − 11 West = −3, so 3 km West of the start.
Net North-South: 3 North − 3 South = 0.
A's final position is 3 km directly West of the start.
The question asks for the start from A, so reverse the direction.
West reverses to East.

Answer: (A) East

Exam tips

Read the last line first. The reference point decides the answer, and examiners often set the reverse as a trap option.
Skip any question with more than six moves if you are short of time. With 0.25 negative marking, guess only after you eliminate at least two options.
Use sign elimination: once you know the net signs, cross out options with the wrong quadrant.
Check turn words carefully. 'Left' and 'right' are relative to the walker's current heading, but 'turns towards North' is absolute.
Practise past-style questions until a 3-move problem takes under 40 seconds.

Practice questions from Direction Tests

Relative Position and Direction Between Two Points: frequently asked questions

How do I find the direction of A from B?

Treat B as the origin and find where A lies by adding the net north-south and east-west shifts from B to A. The signs give the direction. For example, A being north and east of B means A is North-East of B.

If A is North-East of B, where is B from A?

B is South-West of A. Every direction reverses to its opposite when you swap the reference point.

How do left and right turns work?

They depend on the way the person is facing. Facing North, right is East and left is West. Facing East, right is South and left is North. A right turn is a clockwise quarter turn and a left turn is anticlockwise.

Do I need Pythagoras in these questions?

Only when the question also asks for the distance between start and end. For direction alone, the net shifts are enough.