Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 520 · 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 (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
2. 2.What is the distance between the points (4, 9) and (16, 18)? (a) 225 (b) 16 (c) 15 (d) 21
3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
4. 4.What is the midpoint of the line joining (3, 3) and (9, 5)? (a) (3, 1) (b) (6, 4) (c) (12, 8) (d) (4, 6)
5. 5.What is the midpoint of the line joining (9, 4) and (13, 14)? (a) (9, 11) (b) (22, 18) (c) (2, 5) (d) (11, 9)
6. 6.In which quadrant does the point (−6, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
7. 7.What is the midpoint of the line joining (0, 2) and (10, 6)? (a) (5, 2) (b) (10, 8) (c) (5, 4) (d) (4, 5)
8. 8.What is the distance between the points (2, 9) and (6, 12)? (a) 25 (b) 6 (c) 7 (d) 5
9. 9.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
10. 10.What is the midpoint of the line joining (0, 14) and (2, 4)? (a) (2, 18) (b) (1, 5) (c) (1, 9) (d) (9, 1)
11. 11.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
12. 12.What is the midpoint of the line joining (6, 11) and (18, 3)? (a) (24, 14) (b) (12, 7) (c) (6, 4) (d) (7, 12)
13. 13.In which quadrant does the point (−2, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
14. 14.What is the midpoint of the line joining (9, 9) and (11, 7)? (a) (1, 1) (b) (8, 10) (c) (10, 8) (d) (20, 16)
15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
16. 16.What is the distance between the points (9, 4) and (33, 11)? (a) 31 (b) 26 (c) 25 (d) 625
17. 17.What is the distance between the points (8, 9) and (20, 18)? (a) 16 (b) 21 (c) 225 (d) 15
18. 18.What is the midpoint of the line joining (6, 4) and (10, 14)? (a) (16, 18) (b) (9, 8) (c) (2, 5) (d) (8, 9)
19. 19.What is the midpoint of the line joining (9, 0) and (13, 4)? (a) (2, 11) (b) (2, 2) (c) (11, 2) (d) (22, 4)
20. 20.What is the midpoint of the line joining (4, 1) and (14, 9)? (a) (18, 10) (b) (9, 5) (c) (5, 4) (d) (5, 9)
21. 21.What is the distance between the points (9, 14) and (18, 2)? (a) 225 (b) 21 (c) 15 (d) 16
22. 22.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
23. 23.In which quadrant does the point (9, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
24. 24.What is the distance between the points (8, 1) and (16, 16)? (a) 18 (b) 289 (c) 23 (d) 17
25. 25.What is the distance between the points (5, 8) and (10, 20)? (a) 13 (b) 17 (c) 14 (d) 169
26. 26.What is the distance between the points (0, 1) and (8, 16)? (a) 23 (b) 18 (c) 17 (d) 289
27. 27.In which quadrant does the point (−9, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
28. 28.In which quadrant does the point (4, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
29. 29.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
30. 30.What is the distance between the points (7, 17) and (19, 1)? (a) 28 (b) 400 (c) 21 (d) 20
31. 31.In which quadrant does the point (−3, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
33. 33.In which quadrant does the point (1, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
34. 34.In which quadrant does the point (5, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
35. 35.What is the distance between the points (3, 1) and (7, 4)? (a) 7 (b) 5 (c) 6 (d) 25
36. 36.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
37. 37.What is the distance between the points (7, 7) and (23, 19)? (a) 28 (b) 400 (c) 20 (d) 21
38. 38.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
39. 39.What is the midpoint of the line joining (1, 14) and (9, 2)? (a) (5, 8) (b) (4, 6) (c) (8, 5) (d) (10, 16)
40. 40.In which quadrant does the point (−7, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant

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