Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 641 · 40 questions

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

1. 1.In which quadrant does the point (5, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
2. 2.In which quadrant does the point (−1, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
3. 3.What is the distance between the points (9, 12) and (12, 8)? (a) 7 (b) 5 (c) 6 (d) 25
4. 4.In which quadrant does the point (−5, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
5. 5.What is the midpoint of the line joining (1, 10) and (13, 4)? (a) (6, 3) (b) (8, 7) (c) (7, 7) (d) (14, 14)
6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
7. 7.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
8. 8.In which quadrant does the point (2, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
9. 9.In which quadrant does the point (3, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
10. 10.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
12. 12.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
13. 13.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
14. 14.What is the midpoint of the line joining (10, 8) and (14, 0)? (a) (12, 4) (b) (2, 4) (c) (4, 12) (d) (24, 8)
15. 15.What is the distance between the points (8, 0) and (20, 9)? (a) 21 (b) 15 (c) 225 (d) 16
16. 16.What is the midpoint of the line joining (2, 4) and (12, 2)? (a) (7, 3) (b) (14, 6) (c) (5, 1) (d) (3, 7)
17. 17.In which quadrant does the point (−8, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
18. 18.What is the distance between the points (7, 0) and (31, 7)? (a) 31 (b) 25 (c) 625 (d) 26
19. 19.What is the midpoint of the line joining (1, 2) and (9, 14)? (a) (10, 16) (b) (8, 5) (c) (5, 8) (d) (4, 6)
20. 20.In which quadrant does the point (−9, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
21. 21.In which quadrant does the point (9, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
22. 22.What is the distance between the points (8, 3) and (20, 8)? (a) 169 (b) 13 (c) 17 (d) 14
23. 23.In which quadrant does the point (−2, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
25. 25.What is the midpoint of the line joining (7, 0) and (9, 8)? (a) (16, 8) (b) (8, 4) (c) (1, 4) (d) (4, 8)
26. 26.What is the midpoint of the line joining (1, 12) and (5, 4)? (a) (8, 3) (b) (6, 16) (c) (2, 4) (d) (3, 8)
27. 27.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
28. 28.In which quadrant does the point (−7, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
29. 29.What is the distance between the points (8, 16) and (24, 4)? (a) 400 (b) 20 (c) 21 (d) 28
30. 30.What is the midpoint of the line joining (8, 6) and (12, 14)? (a) (2, 4) (b) (11, 10) (c) (10, 10) (d) (20, 20)
31. 31.In which quadrant does the point (8, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
32. 32.In which quadrant does the point (7, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
33. 33.What is the distance between the points (1, 9) and (4, 13)? (a) 5 (b) 6 (c) 7 (d) 25
34. 34.In which quadrant does the point (−2, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the distance between the points (4, 28) and (11, 4)? (a) 25 (b) 26 (c) 625 (d) 31
36. 36.What is the distance between the points (5, 6) and (10, 18)? (a) 13 (b) 14 (c) 169 (d) 17
37. 37.What is the distance between the points (8, 7) and (16, 22)? (a) 18 (b) 17 (c) 289 (d) 23
38. 38.What is the distance between the points (6, 5) and (18, 0)? (a) 169 (b) 14 (c) 13 (d) 17
39. 39.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
40. 40.What is the distance between the points (3, 6) and (8, 18)? (a) 169 (b) 14 (c) 13 (d) 17

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