Coordinate Geometry Worksheet for Maths Olympiad

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

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