Keep a fixed compass

Draw N at the top, E to the right, S at the bottom and W to the left. Record each leg as a signed vertical or horizontal displacement. North and south can cancel; east and west can cancel. If a person goes 7 km east and 3 km west, the net horizontal displacement is 4 km east, even though the distance travelled is 10 km. The distinction between total distance and straight-line displacement is central.

Turns are relative to the facing direction

“Turn right” is not always east. A person facing south who turns right faces west. Keep an arrow showing the current facing direction and rotate it 90 degrees for a right or left turn. A U-turn reverses it by 180 degrees. On a long route, update facing direction after each turn before adding the next displacement. If the item asks for the direction from the final point *back to* the starting point, reverse both the north-south and east-west signs.

Worked route

A candidate walks 8 m north, 5 m east and 2 m south. Net movement is 6 m north and 5 m east, so the final point is north-east of the start. Straight-line distance is √(6² + 5²) = √61 m; distance walked is 15 m. Do not add legs to answer a shortest-distance question. When net movements make a 3–4–5 triangle or a scaled version of it, you can find distance quickly without a calculator.

Diagram habits

Choose a scale that fits the page but keep the cardinal directions exact. Mark the start as O and final position as F. A route may cross itself; the drawing's precise lengths are less important than signed totals. In the practice set, rewrite each right or left turn as a compass direction before moving on. Check whether the question asks facing, location, total travel or shortest separation; those are four different outputs from one route.

Practice — 50 questions

Attempt every item before reading the answers below. Figure questions require the printed or on-screen diagram.

1. Vikram is facing East. He turns 90° anti-clockwise, then turns 270° anti-clockwise, then turns 90° clockwise. Which direction is Vikram facing now?

A. South B. East C. North D. West

2. Rohit starts from point A and drives 12 km towards the West, then turns right and goes 7 km, and finally turns right and goes 12 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 6 km, North B. 7 km, North C. 7 km, South D. 7 km, West

3. Karan starts from point A and drives 4 km towards the West, then turns right and goes 6 km, then turns right and goes 11 km, and finally turns right and goes 6 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 9 km, East B. 7 km, North C. 7 km, West D. 7 km, East

4. Priya starts from point A and walks 12 km towards the East, then turns right and goes 7 km, then turns left and goes 10 km, and finally turns left and goes 7 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 21 km, East B. 23 km, East C. 22 km, West D. 22 km, East

5. At the time of sunset, Meena is standing facing the sun. In which direction does Meena's shadow fall?

A. South B. West C. North D. East

6. At the time of sunrise, Sanjay is standing facing the sun. In which direction does Sanjay's shadow fall?

A. North B. South C. East D. West

7. At the time of sunset, Anjali is standing facing the sun. In which direction does Anjali's shadow fall?

A. South B. East C. North D. West

8. Anjali is facing North. He turns 90° anti-clockwise, then turns 90° anti-clockwise, then turns 180° clockwise. Which direction is Anjali facing now?

A. West B. South C. East D. North

9. Kavita starts from point A and drives 3 km towards the South, then turns right and goes 9 km, and finally turns right and goes 3 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 9 km, East B. 9 km, West C. 11 km, West D. 8 km, West

10. Rahul starts from point A and walks 14 km towards the East, then turns right and goes 9 km, and finally turns right and goes 14 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 9 km, North B. 11 km, South C. 10 km, North D. 9 km, South

11. Sneha is facing North. He turns 270° clockwise, then turns 90° clockwise, then turns 90° clockwise. Which direction is Sneha facing now?

A. West B. North C. South D. East

12. Pooja starts from point A and drives 13 km towards the North, then turns right and goes 14 km, then turns right and goes 13 km, and finally turns left and goes 8 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 22 km, South B. 22 km, East C. 24 km, East D. 22 km, West

13. Sanjay is facing West. He turns 90° clockwise, then turns 180° anti-clockwise, then turns 90° anti-clockwise. Which direction is Sanjay facing now?

A. South B. North C. East D. West

14. Suresh starts from point A and drives 12 km towards the North, then turns right and goes 10 km, and finally turns right and goes 12 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 10 km, East B. 10 km, South C. 10 km, West D. 11 km, West

15. Divya starts from point A and drives 8 km towards the South, then turns right and goes 3 km, then turns left and goes 4 km, and finally turns left and goes 3 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 12 km, North B. 14 km, South C. 12 km, South D. 12 km, East

16. Pooja starts from point A and walks 13 km towards the South, then turns right and goes 8 km, then turns right and goes 16 km, then turns right and goes 3 km, and finally turns right and goes 3 km to stop at point P. How far (shortest distance) and in which direction should she travel to reach point A again? (All turns are 90° turns.)

A. 6 km, East B. 5 km, West C. 4 km, East D. 5 km, East

17. Ritu walks 7 km towards West, then turns right and walks 24 km. What is the shortest distance between Ritu's starting point and current position?

A. 25 km B. 31 km C. 7 km D. 24 km

18. Meena starts walking towards East and walks 8 km, then turns left and walks another 8 km. In which direction from the starting point is Meena now?

A. North-West B. South-West C. North-East D. South-East

19. Rahul is facing East. He turns 90° anti-clockwise, then turns 180° clockwise, then turns 270° anti-clockwise, then turns 90° anti-clockwise. Which direction is Rahul facing now?

A. West B. East C. North D. South

20. Ritu starts from point A and drives 5 km towards the West, then turns left and goes 2 km, then turns left and goes 5 km, and finally turns right and goes 14 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 16 km, West B. 16 km, North C. 16 km, South D. 18 km, South

21. Rahul walks 12 km towards West, then turns left and walks 9 km. What is the shortest distance between Rahul's starting point and current position?

A. 9 km B. 21 km C. 15 km D. 12 km

22. Aman starts from point A and drives 5 km towards the North, then turns right and goes 14 km, then turns right and goes 6 km, then turns right and goes 14 km, and finally turns right and goes 8 km to stop at point P. How far (shortest distance) and in which direction should he travel to reach point A again? (All turns are 90° turns.)

A. 7 km, East B. 8 km, South C. 7 km, South D. 7 km, North

23. Meena starts from point A and drives 8 km towards the West, then turns right and goes 7 km, then turns left and goes 11 km, then turns left and goes 7 km, and finally turns left and goes 14 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 5 km, West B. 4 km, West C. 7 km, West D. 5 km, East

24. Meena is facing West. He turns 270° clockwise, then turns 90° anti-clockwise, then turns 180° clockwise, then turns 90° clockwise. Which direction is Meena facing now?

A. East B. South C. North D. West

25. Vikram starts from point A and walks 12 km towards the South, then turns left and goes 11 km, then turns left and goes 22 km, then turns left and goes 10 km, and finally turns left and goes 10 km to stop at point P. How far (shortest distance) and in which direction should he travel to reach point A again? (All turns are 90° turns.)

A. 1 km, West B. 3 km, West C. 1 km, East D. 2 km, West

26. Manoj starts from point A and drives 6 km towards the South, then turns left and goes 3 km, then turns left and goes 16 km, then turns left and goes 3 km, and finally turns left and goes 6 km to stop at point P. How far (shortest distance) and in which direction should he travel to reach point A again? (All turns are 90° turns.)

A. 4 km, West B. 4 km, South C. 4 km, North D. 6 km, South

27. Manoj starts from point A and walks 7 km towards the West, then turns right and goes 10 km, then turns right and goes 11 km, then turns right and goes 10 km, and finally turns right and goes 11 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 7 km, North B. 7 km, East C. 7 km, West D. 9 km, West

28. Priya is facing West. He turns 180° anti-clockwise, then turns 90° anti-clockwise, then turns 180° clockwise, then turns 90° anti-clockwise. Which direction is Priya facing now?

A. West B. South C. North D. East

29. Sneha starts from point A and drives 2 km towards the North, then turns right and goes 13 km, then turns right and goes 4 km, then turns right and goes 14 km, and finally turns right and goes 2 km to stop at point P. How far (shortest distance) and in which direction should she travel to reach point A again? (All turns are 90° turns.)

A. 1 km, East B. 1 km, West C. 2 km, West D. 1 km, North

30. Priya starts walking towards East and walks 8 km, then turns right and walks another 8 km. In which direction from the starting point is Priya now?

A. South-East B. North-West C. North-East D. South-West

31. Anjali starts walking towards South and walks 6 km, then turns left and walks another 6 km. In which direction from the starting point is Anjali now?

A. North-West B. South-East C. South-West D. North-East

32. Sneha starts from point A and drives 14 km towards the West, then turns right and goes 12 km, then turns right and goes 23 km, then turns right and goes 16 km, and finally turns right and goes 9 km to stop at point P. How far (shortest distance) and in which direction should she travel to reach point A again? (All turns are 90° turns.)

A. 5 km, South B. 4 km, South C. 6 km, North D. 4 km, North

33. Kavita starts from point A and drives 15 km towards the West, then turns left and goes 7 km, then turns left and goes 11 km, then turns left and goes 7 km, and finally turns left and goes 10 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 16 km, West B. 14 km, West C. 14 km, East D. 13 km, West

34. Aman starts from point A and walks 10 km towards the East, then turns right and goes 8 km, then turns right and goes 3 km, then turns right and goes 8 km, and finally turns right and goes 7 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 14 km, South B. 15 km, East C. 14 km, East D. 14 km, West

35. Neha starts from point A and walks 2 km towards the South, then turns right and goes 7 km, then turns right and goes 5 km, then turns right and goes 7 km, and finally turns right and goes 4 km to stop at point P. How far (shortest distance) and in which direction should she travel to reach point A again? (All turns are 90° turns.)

A. 1 km, South B. 3 km, North C. 2 km, South D. 1 km, North

36. Pooja starts from point A and drives 9 km towards the West, then turns right and goes 2 km, then turns right and goes 12 km, then turns right and goes 14 km, and finally turns right and goes 3 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 12 km, South B. 12 km, East C. 12 km, North D. 14 km, South

37. Priya starts from point A and walks 9 km towards the East, then turns right and goes 7 km, then turns right and goes 8 km, then turns right and goes 7 km, and finally turns right and goes 11 km to stop at point P. How far (shortest distance) and in which direction should she travel to reach point A again? (All turns are 90° turns.)

A. 12 km, West B. 12 km, East C. 14 km, West D. 12 km, North

38. Anjali starts walking towards South and walks 6 km, then turns right and walks another 6 km. In which direction from the starting point is Anjali now?

A. North-East B. North-West C. South-East D. South-West

39. Priya is facing South. He turns 180° anti-clockwise, then turns 270° clockwise, then turns 180° clockwise, then turns 90° clockwise. Which direction is Priya facing now?

A. South B. North C. West D. East

40. Suresh starts walking towards South and walks 8 km, then turns left and walks another 8 km. In which direction from the starting point is Suresh now?

A. North-West B. South-West C. South-East D. North-East

41. Anjali walks 5 km towards East, then turns left and walks 6 km, then turns right and walks 3 km. What is the shortest distance between Anjali's starting point and current position?

A. 9 km B. 10 km C. 11 km D. 8 km

42. Meena is facing North. He turns 90° anti-clockwise, then turns 270° anti-clockwise, then turns 90° anti-clockwise, then turns 90° clockwise, then turns 270° anti-clockwise. Which direction is Meena facing now?

A. West B. North C. South D. East

43. Neha starts from point A and walks 8 km towards the North, then turns right and goes 2 km, then turns right and goes 10 km, then turns right and goes 3 km, and finally turns right and goes 2 km to stop at point P. How far (shortest distance) and in which direction should she travel to reach point A again? (All turns are 90° turns.)

A. 1 km, West B. 1 km, East C. 1 km, South D. 2 km, West

44. Kavita walks 5 km towards North, then turns left and walks 12 km, then turns right and walks 4 km. What is the shortest distance between Kavita's starting point and current position?

A. 15 km B. 16 km C. 17 km D. 9 km

45. Ritu is facing East. He turns 180° anti-clockwise, then turns 90° clockwise, then turns 90° anti-clockwise, then turns 270° anti-clockwise, then turns 270° anti-clockwise. Which direction is Ritu facing now?

A. West B. East C. South D. North

46. Kavita starts from point A and drives 14 km towards the East, then turns left and goes 13 km, then turns left and goes 19 km, then turns left and goes 4 km, and finally turns left and goes 5 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 9 km, West B. 9 km, North C. 10 km, North D. 9 km, South

47. Meena starts from point A and walks 11 km towards the East, then turns right and goes 8 km, then turns right and goes 22 km, then turns right and goes 9 km, and finally turns right and goes 11 km to stop at point P. What is the shortest distance of point P from point A, and in which direction is P from A? (All turns are 90° turns.)

A. 3 km, North B. 2 km, North C. 1 km, North D. 1 km, South

48. Rahul starts from point A and walks 6 km towards the South, then turns left and goes 3 km, then turns left and goes 9 km, then turns left and goes 3 km, and finally turns left and goes 6 km to stop at point P. How far (shortest distance) and in which direction should he travel to reach point A again? (All turns are 90° turns.)

A. 3 km, South B. 2 km, North C. 4 km, South D. 3 km, North

49. Manoj starts from point A and drives 2 km towards the South, then turns left and goes 8 km, then turns left and goes 11 km, then turns left and goes 8 km, and finally turns left and goes 10 km to stop at point P. How far (shortest distance) and in which direction should he travel to reach point A again? (All turns are 90° turns.)

A. 1 km, West B. 1 km, South C. 1 km, North D. 2 km, South

50. Sanjay starts walking towards West and walks 4 km, then turns left and walks another 4 km. In which direction from the starting point is Sanjay now?

A. South-West B. South-East C. North-East D. North-West

Answers and explanations

After checking the key, explain the rule or diagram transformation to yourself before moving on.

1. A. Starting from East and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of South.

APRS26-07-01 | Facing direction | Easy

2. B. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 12 − West 12 = 0 (no east-west shift). Net north-south: North 7 − South 0 = 7 (7 km North). So P is 7 km straight North of A. He is at point P; answer: 7 km, North.

APRS26-07-02 | Distance and direction from start | Easy

3. D. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 11 − West 4 = 7 (7 km East). Net north-south: North 6 − South 6 = 0 (no north-south shift). So P is 7 km straight East of A. He is at point P; answer: 7 km, East.

APRS26-07-03 | Distance and direction from start | Easy

4. D. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 22 − West 0 = 22 (22 km East). Net north-south: North 7 − South 7 = 0 (no north-south shift). So P is 22 km straight East of A. She is at point P; answer: 22 km, East.

APRS26-07-04 | Distance and direction from start | Easy

5. D. The sun rises in the East and sets in the West. At sunset, facing the sun means the shadow falls directly behind — towards the East.

APRS26-07-05 | Shadow direction | Easy

6. D. The sun rises in the East and sets in the West. At sunrise, facing the sun means the shadow falls directly behind — towards the West.

APRS26-07-06 | Shadow direction | Easy

7. B. The sun rises in the East and sets in the West. At sunset, facing the sun means the shadow falls directly behind — towards the East.

APRS26-07-07 | Shadow direction | Easy

8. D. Starting from North and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of North.

APRS26-07-08 | Facing direction | Easy

9. B. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 0 − West 9 = -9 (9 km West). Net north-south: North 3 − South 3 = 0 (no north-south shift). So P is 9 km straight West of A. She is at point P; answer: 9 km, West.

APRS26-07-09 | Distance and direction from start | Easy

10. D. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 14 − West 14 = 0 (no east-west shift). Net north-south: North 0 − South 9 = -9 (9 km South). So P is 9 km straight South of A. He is at point P; answer: 9 km, South.

APRS26-07-10 | Distance and direction from start | Easy

11. D. Starting from North and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of East.

APRS26-07-11 | Facing direction | Easy

12. B. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 22 − West 0 = 22 (22 km East). Net north-south: North 13 − South 13 = 0 (no north-south shift). So P is 22 km straight East of A. She is at point P; answer: 22 km, East.

APRS26-07-12 | Distance and direction from start | Easy

13. C. Starting from West and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of East.

APRS26-07-13 | Facing direction | Easy

14. A. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 10 − West 0 = 10 (10 km East). Net north-south: North 12 − South 12 = 0 (no north-south shift). So P is 10 km straight East of A. He is at point P; answer: 10 km, East.

APRS26-07-14 | Distance and direction from start | Easy

15. C. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 3 − West 3 = 0 (no east-west shift). Net north-south: North 0 − South 12 = -12 (12 km South). So P is 12 km straight South of A. She is at point P; answer: 12 km, South.

APRS26-07-15 | Distance and direction from start | Easy

16. D. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 3 − West 8 = -5 (5 km West). Net north-south: North 16 − South 16 = 0 (no north-south shift). So P is 5 km straight West of A. To return to A she must travel the same 5 km in the opposite direction, i.e. towards the East. She is at point P; answer: 5 km, East.

APRS26-07-16 | Distance and direction from start | Medium

17. A. The two legs (7 km and 24 km) are at right angles to each other, forming a right triangle. By the Pythagorean theorem, the direct distance is √(7² + 24²) = 25 km.

APRS26-07-17 | Distance from start | Medium

18. C. Since both legs are equal (8 km each) and at right angles, the resultant position lies exactly on the diagonal North-East of the starting point.

APRS26-07-18 | Direction from start | Medium

19. D. Starting from East and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of South.

APRS26-07-19 | Facing direction | Medium

20. C. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 5 − West 5 = 0 (no east-west shift). Net north-south: North 0 − South 16 = -16 (16 km South). So P is 16 km straight South of A. She is at point P; answer: 16 km, South.

APRS26-07-20 | Distance and direction from start | Medium

21. C. The two legs (12 km and 9 km) are at right angles to each other, forming a right triangle. By the Pythagorean theorem, the direct distance is √(12² + 9²) = 15 km.

APRS26-07-21 | Distance from start | Medium

22. C. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 14 − West 14 = 0 (no east-west shift). Net north-south: North 13 − South 6 = 7 (7 km North). So P is 7 km straight North of A. To return to A he must travel the same 7 km in the opposite direction, i.e. towards the South. He is at point P; answer: 7 km, South.

APRS26-07-22 | Distance and direction from start | Medium

23. A. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 14 − West 19 = -5 (5 km West). Net north-south: North 7 − South 7 = 0 (no north-south shift). So P is 5 km straight West of A. She is at point P; answer: 5 km, West.

APRS26-07-23 | Distance and direction from start | Medium

24. C. Starting from West and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of North.

APRS26-07-24 | Facing direction | Medium

25. A. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 11 − West 10 = 1 (1 km East). Net north-south: North 22 − South 22 = 0 (no north-south shift). So P is 1 km straight East of A. To return to A he must travel the same 1 km in the opposite direction, i.e. towards the West. He is at point P; answer: 1 km, West.

APRS26-07-25 | Distance and direction from start | Medium

26. B. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 3 − West 3 = 0 (no east-west shift). Net north-south: North 16 − South 12 = 4 (4 km North). So P is 4 km straight North of A. To return to A he must travel the same 4 km in the opposite direction, i.e. towards the South. He is at point P; answer: 4 km, South.

APRS26-07-26 | Distance and direction from start | Medium

27. C. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 11 − West 18 = -7 (7 km West). Net north-south: North 10 − South 10 = 0 (no north-south shift). So P is 7 km straight West of A. He is at point P; answer: 7 km, West.

APRS26-07-27 | Distance and direction from start | Medium

28. D. Starting from West and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of East.

APRS26-07-28 | Facing direction | Medium

29. A. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 13 − West 14 = -1 (1 km West). Net north-south: North 4 − South 4 = 0 (no north-south shift). So P is 1 km straight West of A. To return to A she must travel the same 1 km in the opposite direction, i.e. towards the East. She is at point P; answer: 1 km, East.

APRS26-07-29 | Distance and direction from start | Medium

30. A. Since both legs are equal (8 km each) and at right angles, the resultant position lies exactly on the diagonal South-East of the starting point.

APRS26-07-30 | Direction from start | Medium

31. B. Since both legs are equal (6 km each) and at right angles, the resultant position lies exactly on the diagonal South-East of the starting point.

APRS26-07-31 | Direction from start | Medium

32. D. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 23 − West 23 = 0 (no east-west shift). Net north-south: North 12 − South 16 = -4 (4 km South). So P is 4 km straight South of A. To return to A she must travel the same 4 km in the opposite direction, i.e. towards the North. She is at point P; answer: 4 km, North.

APRS26-07-32 | Distance and direction from start | Medium

33. B. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 11 − West 25 = -14 (14 km West). Net north-south: North 7 − South 7 = 0 (no north-south shift). So P is 14 km straight West of A. She is at point P; answer: 14 km, West.

APRS26-07-33 | Distance and direction from start | Medium

34. C. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 17 − West 3 = 14 (14 km East). Net north-south: North 8 − South 8 = 0 (no north-south shift). So P is 14 km straight East of A. He is at point P; answer: 14 km, East.

APRS26-07-34 | Distance and direction from start | Medium

35. D. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 7 − West 7 = 0 (no east-west shift). Net north-south: North 5 − South 6 = -1 (1 km South). So P is 1 km straight South of A. To return to A she must travel the same 1 km in the opposite direction, i.e. towards the North. She is at point P; answer: 1 km, North.

APRS26-07-35 | Distance and direction from start | Medium

36. A. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 12 − West 12 = 0 (no east-west shift). Net north-south: North 2 − South 14 = -12 (12 km South). So P is 12 km straight South of A. She is at point P; answer: 12 km, South.

APRS26-07-36 | Distance and direction from start | Medium

37. A. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 20 − West 8 = 12 (12 km East). Net north-south: North 7 − South 7 = 0 (no north-south shift). So P is 12 km straight East of A. To return to A she must travel the same 12 km in the opposite direction, i.e. towards the West. She is at point P; answer: 12 km, West.

APRS26-07-37 | Distance and direction from start | Medium

38. D. Since both legs are equal (6 km each) and at right angles, the resultant position lies exactly on the diagonal South-West of the starting point.

APRS26-07-38 | Direction from start | Medium

39. A. Starting from South and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of South.

APRS26-07-39 | Facing direction | Medium

40. C. Since both legs are equal (8 km each) and at right angles, the resultant position lies exactly on the diagonal South-East of the starting point.

APRS26-07-40 | Direction from start | Medium

41. B. The 1st and 3rd legs both lie on the same axis and run the same direction, so they add up: 5 + 3 = 8 km. That combines with the 2nd leg (6 km, at right angles) into a right triangle: √(8² + 6²) = 10 km.

APRS26-07-41 | Distance from start | Difficult

42. D. Starting from North and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of East.

APRS26-07-42 | Facing direction | Difficult

43. B. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 2 − West 3 = -1 (1 km West). Net north-south: North 10 − South 10 = 0 (no north-south shift). So P is 1 km straight West of A. To return to A she must travel the same 1 km in the opposite direction, i.e. towards the East. She is at point P; answer: 1 km, East.

APRS26-07-43 | Distance and direction from start | Difficult

44. A. The 1st and 3rd legs both lie on the same axis and run the same direction, so they add up: 5 + 4 = 9 km. That combines with the 2nd leg (12 km, at right angles) into a right triangle: √(9² + 12²) = 15 km.

APRS26-07-44 | Distance from start | Difficult

45. B. Starting from East and applying each turn in order (clockwise = to the right, anti-clockwise = to the left; 180° reverses, 270° clockwise equals 90° anti-clockwise) gives a final heading of East.

APRS26-07-45 | Facing direction | Difficult

46. B. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 19 − West 19 = 0 (no east-west shift). Net north-south: North 13 − South 4 = 9 (9 km North). So P is 9 km straight North of A. She is at point P; answer: 9 km, North.

APRS26-07-46 | Distance and direction from start | Difficult

47. C. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 22 − West 22 = 0 (no east-west shift). Net north-south: North 9 − South 8 = 1 (1 km North). So P is 1 km straight North of A. She is at point P; answer: 1 km, North.

APRS26-07-47 | Distance and direction from start | Difficult

48. D. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 3 − West 3 = 0 (no east-west shift). Net north-south: North 9 − South 12 = -3 (3 km South). So P is 3 km straight South of A. To return to A he must travel the same 3 km in the opposite direction, i.e. towards the North. He is at point P; answer: 3 km, North.

APRS26-07-48 | Distance and direction from start | Difficult

49. C. Track each leg on a compass grid (a left turn rotates the heading 90° anti-clockwise, a right turn 90° clockwise). Net east-west: East 8 − West 8 = 0 (no east-west shift). Net north-south: North 11 − South 12 = -1 (1 km South). So P is 1 km straight South of A. To return to A he must travel the same 1 km in the opposite direction, i.e. towards the North. He is at point P; answer: 1 km, North.

APRS26-07-49 | Distance and direction from start | Difficult

50. A. Since both legs are equal (4 km each) and at right angles, the resultant position lies exactly on the diagonal South-West of the starting point.

APRS26-07-50 | Direction from start | Difficult