Direction & Distance Notes

Last reviewed 22 Sept 2026 · 5 min read

The compass

North is up, South down, East right, West left, with North-East, South-East, South-West and North-West between them. Each adjacent pair is $45°$ apart, and opposite directions are $180°$ apart.

RememberTurning, once and for all

Facing North: a right turn faces East, a left turn faces West. Facing South: a right turn faces West, a left turn faces East — the reverse of the North case, and the source of most errors. A clockwise turn of $90°$ is a right turn; anticlockwise is a left turn.

A simple way to never slip: draw a small arrow for the direction the person faces, and physically rotate the page when a turn is made.

Drawing the route

Start at a dot and mark the initial direction with an arrow.
Draw each leg roughly to scale — 10 km twice as long as 5 km — so the final picture is honest.
Cancel opposite legs: 10 km north then 4 km south is 6 km north.
What remains is at most one north–south leg and one east–west leg, meeting at a right angle.

Distance and direction of the finish

FormulaNet displacement

If the leftover legs are $a$ (north–south) and $b$ (east–west):

Distance from the start = a^{2} + b^{2}

and the direction is the corner they make — north and east means North-East. When $a = b$ exactly, the direction is the diagonal ( $45°$ ).

The 3-4-5, 5-12-13 and 8-15-17 triples appear constantly, because they give whole-number answers.

Shadows

At sunrise the sun is in the east, so shadows fall to the west; at sunset the sun is in the west and shadows fall to the east. At noon the shadow is negligible or falls north or south depending on the place. So: "In the morning, a man's shadow fell to his left" → his left is west → he faces north.

Worked examples

Worked ExampleExample 1 — a plain route

A man walks 4 km north, then 3 km east. How far is he from the start, and in which direction?

Solution. $4^{2} + 3^{2} =$ 5 km, to the North-East of the start.

Worked ExampleExample 2 — cancelling legs

A walks 10 km south, 6 km east, 4 km north and 6 km west. Where is he?

Solution. North–south: $10 - 4 = 6$ km south. East–west: $6 - 6 = 0$ . He is 6 km south of the start.

Worked ExampleExample 3 — a turn while facing south

A man faces south, turns right, walks 5 km, turns left and walks 3 km. In which direction is he from the start?

Solution. Facing south, a right turn faces west; 5 km west, then a left turn faces south; 3 km south. He is to the South-West.

Worked ExampleExample 4 — distance with a triple

B walks 12 km north, 5 km west. How far is he from the start?

Solution. $144 + 25 =$ 13 km (North-West of the start).

Worked ExampleExample 5 — several turns

Starting facing east, a person turns left, walks 4 km, turns right, walks 3 km, turns right, walks 4 km. Where is he?

Solution. Left from east is north (4 km north); right is east (3 km east); right is south (4 km south). North and south cancel → 3 km east of the start.

Worked ExampleExample 6 — the final facing

A man facing north turns $135°$ clockwise, then $180°$ anticlockwise. Which direction is he facing?

Solution. $135°$ clockwise from north is South-East; $180°$ back the other way is North-West.

Worked ExampleExample 7 — a shadow

Early in the morning, Ravi's shadow fell exactly to his right. Which way was he facing?

Solution. In the morning shadows fall west, so his right is west → he faces south.

Worked ExampleExample 8 — two people

P and Q start from the same point. P walks 6 km east; Q walks 8 km north. How far apart are they?

Solution. $36 + 64 =$ 10 km.

Worked ExampleExample 9 — distance in one direction only

A person walks 5 km north, 3 km east, 5 km south and 3 km west. How far is he from the start?

Solution. Every leg is cancelled → 0 km; he is back at the start.

Worked ExampleExample 10 — a bearing in words

From the start, a man walks 7 km east, then 7 km north. What is his direction from the start?

Solution. Equal legs east and north → exactly North-East, at $98 \approx 9.9$ km.

Frequently tested points

Facing south reverses the meaning of left and right compared with facing north.
Clockwise is right, anticlockwise is left.
Cancel opposite legs first; what remains is a right-angled triangle.
Net distance $= a^{2} + b^{2}$ , and equal legs give an exact diagonal direction.
Morning shadows fall west, evening shadows east.
"How far" asks for straight-line distance, not the distance walked.

Common MistakeCommon mistakes

Applying "right turn = east" while the person faces some other direction.
Adding the legs walked instead of finding the straight-line displacement.
Mixing up $45°$ (one step round the compass) with $90°$ .
Reading "shadow to his left" as the sun being on his left.
Forgetting to update the facing direction after each turn.

Revision SummaryChapter summary

Directions questions are drawing exercises on a compass grid, with the facing arrow updated at every turn.
Left and right depend on the direction faced, and reverse between north and south.
Opposite legs cancel, leaving a right-angled triangle whose hypotenuse is the answer.
Equal north–south and east–west legs give an exact diagonal direction.
Shadow questions rest on one fact: the sun rises in the east, so morning shadows point west.

Downloaded from civilgyantests.com · Not for resale. Verify every code clause and date against the official source.

Direction & Distance