Direction Sense
Direction sense is coordinate geometry in disguise. Fix north as up on your scratch paper, plot each move as a step, and the final answer is just where the point ends up.
Mental model
Direction questions are geometry, not language. Always draw north at the TOP of your rough sheet before the first move, and mark every turn as a fresh arrow — 'left' and 'right' are relative to the walker's current facing, which is what most wrong answers get backwards. Track only two running totals, net north-south and net east-west; the final displacement is the hypotenuse, so distance = square root of (net vertical squared + net horizontal squared). Right-angle triples 3-4-5, 6-8-10 and 5-12-13 solve almost every such question in one line.
Associations
A short trigger on the left, everything it pulls with it on the right.
Left turn and right turn depend on facing direction, not on a fixed map.
If you are facing north and turn right, you now face east. If you are facing south and turn right, you now face west. The turn is always relative to where you are currently facing — draw an arrow for current facing direction and update it after every turn.
Distance questions collapse to the Pythagorean theorem when the path has a right-angle turn.
'Walked 3 km north, then 4 km east — how far from the start?' is just a 3-4-5 right triangle. Recognising this shortcut saves plotting the whole path when only the final displacement is asked.
Things to remember
The night-before list. Short enough to recall cold.
- 1A right turn from north faces east; from east faces south; from south faces west; from west faces north — the cycle repeats clockwise.
- 2A left turn cycles anticlockwise: north to west to south to east and back to north.
- 3At sunrise, a person facing the sun is facing east; their shadow falls to the west, behind them.
- 4Net displacement (straight-line distance from start to end) is different from total distance walked — a question asking 'how far from the starting point' wants displacement, not the path length.
In detail
- Shortest distance from start to finish = square root of (net north-south distance squared + net east-west distance squared).
- Memorise the Pythagorean triples 3-4-5, 6-8-10, 5-12-13 and 9-12-15; exam figures are almost always built on one of them.
- Facing north, a right turn gives east and a left turn gives west; facing south, the two swap — this reversal is the classic trap.
- At sunrise the shadow of an object falls towards the west and at sunset towards the east; at noon in the northern hemisphere it falls towards the north.
- Two successive left turns or two successive right turns reverse the original direction; a left followed by a right restores it.
Where people slip
- Do not confuse the direction you are facing with the direction you have travelled from — after several turns these are usually different.
Check yourself
Nothing here is scored — it will not change your mastery figures.
A person walks 3 km north, then turns right and walks 4 km. How far is he from his starting point?
From the question bank
A man walks 10 km to the North, then turns right and walks 5 km. In which direction is he now facing?
From the question bank
A man walks 3 km to the East and then 4 km to the North. How far is he from his starting point?
Books to read
- A Modern Approach to Verbal and Non-Verbal Reasoning — R S Aggarwal
- Analytical Reasoning — M K Pandey
Official sources
Hand-checked official domains only — the notes above carry no links of their own.