Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 843 · 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.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
3. 3.In which quadrant does the point (5, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
4. 4.What is the distance between the points (9, 19) and (21, 3)? (a) 400 (b) 28 (c) 21 (d) 20
5. 5.What is the distance between the points (2, 0) and (5, 4)? (a) 25 (b) 7 (c) 6 (d) 5
6. 6.In which quadrant does the point (9, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
7. 7.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
8. 8.What is the midpoint of the line joining (8, 10) and (14, 12)? (a) (3, 1) (b) (12, 11) (c) (22, 22) (d) (11, 11)
9. 9.What is the midpoint of the line joining (3, 13) and (15, 5)? (a) (6, 4) (b) (10, 9) (c) (9, 9) (d) (18, 18)
10. 10.What is the midpoint of the line joining (9, 11) and (17, 7)? (a) (4, 2) (b) (26, 18) (c) (9, 13) (d) (13, 9)
11. 11.In which quadrant does the point (−5, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
13. 13.What is the distance between the points (5, 10) and (9, 7)? (a) 25 (b) 7 (c) 5 (d) 6
14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
15. 15.What is the midpoint of the line joining (8, 16) and (18, 6)? (a) (5, 5) (b) (11, 13) (c) (26, 22) (d) (13, 11)
16. 16.What is the distance between the points (4, 9) and (16, 14)? (a) 13 (b) 169 (c) 17 (d) 14
17. 17.What is the distance between the points (4, 1) and (12, 16)? (a) 18 (b) 23 (c) 289 (d) 17
18. 18.What is the midpoint of the line joining (7, 0) and (9, 6)? (a) (8, 3) (b) (16, 6) (c) (3, 8) (d) (1, 3)
19. 19.What is the distance between the points (0, 13) and (6, 5)? (a) 14 (b) 100 (c) 10 (d) 11
20. 20.What is the midpoint of the line joining (5, 15) and (17, 7)? (a) (12, 11) (b) (22, 22) (c) (11, 11) (d) (6, 4)
21. 21.What is the distance between the points (9, 5) and (17, 11)? (a) 14 (b) 10 (c) 11 (d) 100
22. 22.In which quadrant does the point (−2, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (−7, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
24. 24.In which quadrant does the point (5, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
25. 25.In which quadrant does the point (7, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.What is the distance between the points (1, 24) and (13, 8)? (a) 20 (b) 21 (c) 28 (d) 400
27. 27.What is the distance between the points (0, 4) and (9, 16)? (a) 15 (b) 16 (c) 21 (d) 225
28. 28.In which quadrant does the point (−3, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
29. 29.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
30. 30.What is the midpoint of the line joining (3, 6) and (7, 8)? (a) (7, 5) (b) (2, 1) (c) (5, 7) (d) (10, 14)
31. 31.In which quadrant does the point (−6, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
32. 32.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
33. 33.What is the distance between the points (8, 7) and (13, 19)? (a) 17 (b) 14 (c) 169 (d) 13
34. 34.What is the midpoint of the line joining (1, 7) and (3, 3)? (a) (1, 2) (b) (2, 5) (c) (5, 2) (d) (4, 10)
35. 35.In which quadrant does the point (−5, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
36. 36.In which quadrant does the point (8, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.What is the distance between the points (8, 16) and (32, 9)? (a) 31 (b) 625 (c) 26 (d) 25
38. 38.What is the distance between the points (7, 5) and (14, 29)? (a) 26 (b) 25 (c) 625 (d) 31
39. 39.In which quadrant does the point (−1, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14

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