Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 594 · 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.In which quadrant does the point (−5, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
2. 2.What is the distance between the points (2, 8) and (26, 1)? (a) 625 (b) 25 (c) 31 (d) 26
3. 3.What is the midpoint of the line joining (2, 10) and (14, 12)? (a) (8, 11) (b) (6, 1) (c) (16, 22) (d) (11, 8)
4. 4.What is the distance between the points (9, 9) and (21, 0)? (a) 225 (b) 21 (c) 15 (d) 16
5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
7. 7.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
9. 9.In which quadrant does the point (−9, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
10. 10.What is the distance between the points (1, 11) and (13, 2)? (a) 15 (b) 16 (c) 225 (d) 21
11. 11.What is the distance between the points (0, 2) and (12, 18)? (a) 21 (b) 400 (c) 20 (d) 28
12. 12.What is the distance between the points (8, 26) and (15, 2)? (a) 26 (b) 25 (c) 31 (d) 625
13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
14. 14.What is the midpoint of the line joining (7, 6) and (15, 0)? (a) (4, 3) (b) (3, 11) (c) (11, 3) (d) (22, 6)
15. 15.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
16. 16.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
17. 17.In which quadrant does the point (−4, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
19. 19.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
20. 20.In which quadrant does the point (3, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
21. 21.In which quadrant does the point (−3, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
22. 22.What is the midpoint of the line joining (4, 2) and (16, 8)? (a) (6, 3) (b) (20, 10) (c) (10, 5) (d) (5, 10)
23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
24. 24.What is the midpoint of the line joining (6, 12) and (8, 0)? (a) (7, 6) (b) (14, 12) (c) (1, 6) (d) (6, 7)
25. 25.In which quadrant does the point (−5, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.What is the distance between the points (5, 1) and (13, 7)? (a) 11 (b) 100 (c) 14 (d) 10
27. 27.In which quadrant does the point (−7, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
28. 28.In which quadrant does the point (7, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
30. 30.In which quadrant does the point (7, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
31. 31.In which quadrant does the point (9, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
32. 32.In which quadrant does the point (3, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
33. 33.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
34. 34.What is the distance between the points (8, 3) and (17, 15)? (a) 15 (b) 16 (c) 21 (d) 225
35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
36. 36.What is the midpoint of the line joining (1, 8) and (13, 10)? (a) (9, 7) (b) (14, 18) (c) (7, 9) (d) (6, 1)
37. 37.What is the distance between the points (5, 14) and (21, 2)? (a) 20 (b) 400 (c) 21 (d) 28
38. 38.In which quadrant does the point (3, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
39. 39.What is the midpoint of the line joining (0, 17) and (12, 9)? (a) (6, 4) (b) (12, 26) (c) (13, 6) (d) (6, 13)
40. 40.In which quadrant does the point (4, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

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