Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 152 · 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, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
3. 3.What is the distance between the points (1, 8) and (25, 15)? (a) 31 (b) 26 (c) 25 (d) 625
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
5. 5.In which quadrant does the point (−1, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
7. 7.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
8. 8.What is the distance between the points (4, 0) and (12, 15)? (a) 17 (b) 23 (c) 18 (d) 289
9. 9.In which quadrant does the point (5, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
10. 10.What is the distance between the points (0, 18) and (5, 6)? (a) 13 (b) 169 (c) 14 (d) 17
11. 11.In which quadrant does the point (−2, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
12. 12.What is the distance between the points (9, 3) and (15, 11)? (a) 14 (b) 100 (c) 10 (d) 11
13. 13.What is the midpoint of the line joining (8, 21) and (10, 9)? (a) (15, 9) (b) (1, 6) (c) (18, 30) (d) (9, 15)
14. 14.What is the distance between the points (3, 10) and (11, 4)? (a) 100 (b) 14 (c) 11 (d) 10
15. 15.What is the midpoint of the line joining (7, 9) and (11, 19)? (a) (18, 28) (b) (2, 5) (c) (14, 9) (d) (9, 14)
16. 16.What is the midpoint of the line joining (2, 7) and (4, 1)? (a) (1, 3) (b) (4, 3) (c) (3, 4) (d) (6, 8)
17. 17.What is the distance between the points (3, 16) and (18, 8)? (a) 23 (b) 18 (c) 17 (d) 289
18. 18.What is the distance between the points (2, 25) and (9, 1)? (a) 31 (b) 625 (c) 26 (d) 25
19. 19.What is the midpoint of the line joining (5, 9) and (17, 13)? (a) (11, 11) (b) (22, 22) (c) (6, 2) (d) (12, 11)
20. 20.What is the distance between the points (0, 20) and (16, 8)? (a) 400 (b) 28 (c) 20 (d) 21
21. 21.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
22. 22.In which quadrant does the point (−8, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
23. 23.What is the midpoint of the line joining (2, 3) and (6, 9)? (a) (4, 6) (b) (2, 3) (c) (6, 4) (d) (8, 12)
24. 24.What is the distance between the points (3, 1) and (11, 7)? (a) 10 (b) 100 (c) 14 (d) 11
25. 25.What is the distance between the points (5, 3) and (9, 6)? (a) 25 (b) 7 (c) 6 (d) 5
26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
27. 27.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
28. 28.What is the distance between the points (6, 2) and (18, 18)? (a) 28 (b) 400 (c) 20 (d) 21
29. 29.In which quadrant does the point (−2, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
30. 30.What is the distance between the points (8, 13) and (32, 6)? (a) 625 (b) 25 (c) 31 (d) 26
31. 31.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
32. 32.What is the distance between the points (5, 9) and (17, 18)? (a) 225 (b) 21 (c) 16 (d) 15
33. 33.What is the midpoint of the line joining (1, 8) and (5, 18)? (a) (6, 26) (b) (2, 5) (c) (13, 3) (d) (3, 13)
34. 34.What is the midpoint of the line joining (5, 3) and (11, 13)? (a) (3, 5) (b) (8, 8) (c) (16, 16) (d) (9, 8)
35. 35.What is the midpoint of the line joining (2, 16) and (10, 8)? (a) (12, 24) (b) (12, 6) (c) (4, 4) (d) (6, 12)
36. 36.What is the midpoint of the line joining (9, 2) and (11, 4)? (a) (10, 3) (b) (3, 10) (c) (1, 1) (d) (20, 6)
37. 37.What is the midpoint of the line joining (0, 6) and (4, 2)? (a) (4, 8) (b) (4, 2) (c) (2, 4) (d) (2, 2)
38. 38.What is the distance between the points (9, 2) and (24, 10)? (a) 17 (b) 18 (c) 23 (d) 289
39. 39.What is the distance between the points (3, 1) and (15, 17)? (a) 20 (b) 28 (c) 400 (d) 21
40. 40.What is the distance between the points (0, 11) and (8, 5)? (a) 10 (b) 100 (c) 11 (d) 14

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