Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 865 · 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.What is the distance between the points (6, 7) and (18, 2)? (a) 14 (b) 13 (c) 169 (d) 17
2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
4. 4.What is the midpoint of the line joining (2, 1) and (12, 9)? (a) (7, 5) (b) (14, 10) (c) (5, 4) (d) (5, 7)
5. 5.What is the distance between the points (2, 14) and (18, 2)? (a) 28 (b) 400 (c) 20 (d) 21
6. 6.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
7. 7.What is the distance between the points (2, 9) and (14, 0)? (a) 21 (b) 15 (c) 16 (d) 225
8. 8.In which quadrant does the point (−4, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
9. 9.What is the distance between the points (1, 9) and (13, 25)? (a) 400 (b) 28 (c) 21 (d) 20
10. 10.What is the distance between the points (0, 24) and (12, 8)? (a) 28 (b) 400 (c) 20 (d) 21
11. 11.What is the distance between the points (9, 3) and (25, 15)? (a) 28 (b) 400 (c) 20 (d) 21
12. 12.In which quadrant does the point (9, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
13. 13.In which quadrant does the point (−5, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
14. 14.What is the midpoint of the line joining (2, 17) and (6, 5)? (a) (2, 6) (b) (4, 11) (c) (8, 22) (d) (11, 4)
15. 15.In which quadrant does the point (−4, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
16. 16.What is the midpoint of the line joining (4, 15) and (14, 3)? (a) (10, 9) (b) (5, 6) (c) (18, 18) (d) (9, 9)
17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
18. 18.What is the distance between the points (1, 4) and (13, 20)? (a) 28 (b) 400 (c) 20 (d) 21
19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
20. 20.What is the distance between the points (5, 21) and (13, 6)? (a) 17 (b) 289 (c) 23 (d) 18
21. 21.What is the midpoint of the line joining (0, 3) and (8, 5)? (a) (4, 1) (b) (5, 4) (c) (4, 4) (d) (8, 8)
22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
23. 23.In which quadrant does the point (−5, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
24. 24.What is the midpoint of the line joining (5, 3) and (17, 13)? (a) (6, 5) (b) (8, 11) (c) (11, 8) (d) (22, 16)
25. 25.What is the midpoint of the line joining (6, 6) and (12, 2)? (a) (4, 9) (b) (9, 4) (c) (18, 8) (d) (3, 2)
26. 26.What is the midpoint of the line joining (1, 14) and (13, 8)? (a) (14, 22) (b) (7, 11) (c) (11, 7) (d) (6, 3)
27. 27.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
28. 28.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
29. 29.What is the distance between the points (6, 14) and (11, 2)? (a) 17 (b) 169 (c) 14 (d) 13
30. 30.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
31. 31.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
32. 32.What is the midpoint of the line joining (3, 5) and (7, 17)? (a) (2, 6) (b) (10, 22) (c) (11, 5) (d) (5, 11)
33. 33.In which quadrant does the point (−2, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
34. 34.In which quadrant does the point (−2, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
35. 35.What is the midpoint of the line joining (9, 9) and (11, 7)? (a) (20, 16) (b) (10, 8) (c) (8, 10) (d) (1, 1)
36. 36.What is the midpoint of the line joining (6, 13) and (8, 9)? (a) (1, 2) (b) (11, 7) (c) (14, 22) (d) (7, 11)
37. 37.What is the distance between the points (6, 8) and (18, 3)? (a) 13 (b) 169 (c) 17 (d) 14
38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
39. 39.What is the midpoint of the line joining (0, 12) and (2, 10)? (a) (11, 1) (b) (1, 1) (c) (2, 22) (d) (1, 11)
40. 40.What is the distance between the points (0, 9) and (3, 13)? (a) 5 (b) 6 (c) 25 (d) 7

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