Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 94 · 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 (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
2. 2.What is the distance between the points (2, 9) and (8, 17)? (a) 14 (b) 100 (c) 11 (d) 10
3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
4. 4.In which quadrant does the point (−9, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.What is the distance between the points (2, 6) and (11, 18)? (a) 15 (b) 21 (c) 16 (d) 225
6. 6.What is the midpoint of the line joining (8, 10) and (18, 16)? (a) (14, 13) (b) (26, 26) (c) (5, 3) (d) (13, 13)
7. 7.What is the midpoint of the line joining (5, 4) and (11, 8)? (a) (16, 12) (b) (8, 6) (c) (6, 8) (d) (3, 2)
8. 8.What is the distance between the points (3, 13) and (8, 1)? (a) 169 (b) 14 (c) 17 (d) 13
9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
10. 10.In which quadrant does the point (−2, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
11. 11.In which quadrant does the point (−1, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
12. 12.In which quadrant does the point (4, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
13. 13.What is the distance between the points (5, 11) and (29, 4)? (a) 26 (b) 25 (c) 31 (d) 625
14. 14.What is the distance between the points (2, 23) and (10, 8)? (a) 289 (b) 18 (c) 17 (d) 23
15. 15.What is the distance between the points (7, 7) and (15, 1)? (a) 100 (b) 14 (c) 10 (d) 11
16. 16.What is the distance between the points (4, 4) and (12, 10)? (a) 10 (b) 11 (c) 100 (d) 14
17. 17.What is the midpoint of the line joining (10, 9) and (14, 11)? (a) (24, 20) (b) (12, 10) (c) (2, 1) (d) (10, 12)
18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
19. 19.What is the midpoint of the line joining (10, 14) and (12, 2)? (a) (8, 11) (b) (22, 16) (c) (1, 6) (d) (11, 8)
20. 20.In which quadrant does the point (−2, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
21. 21.What is the midpoint of the line joining (7, 2) and (19, 4)? (a) (6, 1) (b) (13, 3) (c) (3, 13) (d) (26, 6)
22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
23. 23.In which quadrant does the point (7, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
24. 24.What is the distance between the points (1, 6) and (13, 22)? (a) 400 (b) 28 (c) 20 (d) 21
25. 25.What is the midpoint of the line joining (7, 8) and (13, 14)? (a) (3, 3) (b) (10, 11) (c) (20, 22) (d) (11, 10)
26. 26.What is the midpoint of the line joining (3, 4) and (13, 16)? (a) (16, 20) (b) (8, 10) (c) (10, 8) (d) (5, 6)
27. 27.What is the distance between the points (2, 9) and (7, 21)? (a) 17 (b) 13 (c) 169 (d) 14
28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
29. 29.What is the midpoint of the line joining (6, 11) and (8, 9)? (a) (7, 10) (b) (1, 1) (c) (14, 20) (d) (10, 7)
30. 30.What is the midpoint of the line joining (3, 15) and (9, 3)? (a) (3, 6) (b) (6, 9) (c) (12, 18) (d) (9, 6)
31. 31.In which quadrant does the point (−4, −8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
32. 32.What is the distance between the points (3, 18) and (15, 2)? (a) 400 (b) 28 (c) 20 (d) 21
33. 33.In which quadrant does the point (−7, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
34. 34.What is the distance between the points (8, 32) and (15, 8)? (a) 625 (b) 25 (c) 31 (d) 26
35. 35.What is the midpoint of the line joining (0, 4) and (8, 12)? (a) (4, 4) (b) (4, 8) (c) (8, 16) (d) (8, 4)
36. 36.What is the midpoint of the line joining (10, 7) and (22, 15)? (a) (11, 16) (b) (6, 4) (c) (32, 22) (d) (16, 11)
37. 37.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
38. 38.What is the midpoint of the line joining (8, 5) and (14, 11)? (a) (8, 11) (b) (22, 16) (c) (3, 3) (d) (11, 8)
39. 39.What is the distance between the points (9, 3) and (24, 11)? (a) 18 (b) 289 (c) 23 (d) 17
40. 40.In which quadrant does the point (6, 7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant

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