Direction and Distance — Practice

Question 1

A man walks 3 km north and then 4 km east. How far is he from his starting point?
(a) 4 km (b) 5 km (c) 6 km (d) 7 km

Accepted Answer

(b) 5 km.

Net displacement = √(3² + 4²) = 5 km, in the north-east direction — the 3–4–5 triple.

Question 2

Ram walks 5 km south, turns left and walks 3 km, then turns left again and walks 5 km. In which direction is he now from his starting point?
(a) North (b) South (c) East (d) West

Accepted Answer

(c) East.

Facing south, left = east (3 km); next left = north (5 km, cancelling the southward 5). Net position: 3 km due east of the start.

Question 3

A man facing north turns 90° clockwise and then 135° anticlockwise. Which direction is he facing now?
(a) North-east (b) North-west (c) South-west (d) East

Accepted Answer

(b) North-west.

Net rotation = +90 − 135 = −45°, i.e., 45° anticlockwise from north = north-west.

Question 4

One morning after sunrise, Gopal stood facing a pole whose shadow fell exactly to his right. Which direction was Gopal facing?
(a) North (b) South (c) East (d) West

Accepted Answer

(b) South.

Morning shadows point west (away from the rising eastern sun). West on his right hand means he faces south.

Question 5

A man facing west turns 45° clockwise, then 180°, and then 270° anticlockwise. Which direction does he face now?
(a) South-west (b) North-east (c) South (d) West

Accepted Answer

(a) South-west.

Net = +45 + 180 − 270 = −45°: one 45° step anticlockwise from west, which is south-west (anticlockwise order from west: SW, S, SE…).

Question 6

B is 5 km east of A. C is 5 km north of B. D is 5 km south of C. How far and in which direction is D from A?
(a) 5 km west (b) 5 km east (c) 10 km east (d) 5√2 km north-east

Accepted Answer

(b) 5 km east.

D is 5 km south of C, and C is 5 km north of B — so D coincides with B, which is 5 km east of A. The vertical legs cancel; plotting makes it obvious.

Question 7

A man walks 40 m south, then 20 m west, then 20 m north. How far and in which direction is he from the starting point?
(a) 20 m south-west (b) 20√2 m south-west (c) 20√2 m south-east (d) 40 m south

Accepted Answer

(b) 20√2 m south-west.

Coordinates: (0,0) → (0,−40) → (−20,−40) → (−20,−20). Net (−20, −20): 20 m west and 20 m south → distance √(400+400) = 20√2, direction south-west.

Question 8

Kishan walks 20 m north, turns right and walks 30 m, turns right and walks 20 m, then turns left and walks 10 m. How far is he from his starting point?
(a) 30 m (b) 40 m (c) 50 m (d) 60 m

Accepted Answer

(b) 40 m.

Path: (0,0) → (0,20) → [right = east] (30,20) → [right = south] (30,0) → [left = east] (40,0). The north and south legs cancel; he stands 40 m due east.

Question 9

One evening before sunset, Priya noticed her shadow fell exactly behind her. Which direction was she facing?
(a) East (b) West (c) North (d) South

Accepted Answer

(b) West.

Evening sun is in the west, so shadows point east. The shadow behind her means east is at her back — she faces west (into the setting sun).

Question 10

A clock shows 4:30, and its minute hand points towards the east. In which direction does the hour hand point?
(a) North-east (b) South-east (c) North-west (d) South

Accepted Answer

(a) North-east.

At 4:30 the minute hand is at the 6 mark and the hour hand midway between 4 and 5 — that is, 45° anticlockwise from the minute hand on the dial. The 6 mark points east, and 45° anticlockwise from east is north-east.

Practice — Direction and Distance

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