Coordinate Geometry Worksheet for Maths Olympiad

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

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