Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 525 · 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 midpoint of the line joining (8, 12) and (10, 6)? (a) (18, 18) (b) (10, 9) (c) (9, 9) (d) (1, 3)
2. 2.What is the distance between the points (2, 11) and (14, 2)? (a) 16 (b) 21 (c) 225 (d) 15
3. 3.What is the midpoint of the line joining (0, 1) and (10, 7)? (a) (5, 3) (b) (4, 5) (c) (5, 4) (d) (10, 8)
4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
5. 5.What is the midpoint of the line joining (4, 13) and (10, 7)? (a) (14, 20) (b) (7, 10) (c) (3, 3) (d) (10, 7)
6. 6.What is the distance between the points (5, 8) and (8, 12)? (a) 7 (b) 6 (c) 25 (d) 5
7. 7.What is the distance between the points (1, 1) and (8, 25)? (a) 625 (b) 25 (c) 26 (d) 31
8. 8.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
10. 10.In which quadrant does the point (1, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
11. 11.What is the midpoint of the line joining (9, 5) and (17, 17)? (a) (11, 13) (b) (4, 6) (c) (26, 22) (d) (13, 11)
12. 12.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
13. 13.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
14. 14.What is the distance between the points (5, 16) and (29, 9)? (a) 625 (b) 26 (c) 31 (d) 25
15. 15.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
16. 16.In which quadrant does the point (−2, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
18. 18.What is the midpoint of the line joining (5, 9) and (11, 19)? (a) (8, 14) (b) (14, 8) (c) (16, 28) (d) (3, 5)
19. 19.What is the midpoint of the line joining (9, 2) and (19, 14)? (a) (5, 6) (b) (8, 14) (c) (28, 16) (d) (14, 8)
20. 20.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
21. 21.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
22. 22.What is the midpoint of the line joining (9, 3) and (15, 9)? (a) (3, 3) (b) (24, 12) (c) (6, 12) (d) (12, 6)
23. 23.What is the midpoint of the line joining (9, 1) and (17, 13)? (a) (13, 7) (b) (7, 13) (c) (4, 6) (d) (26, 14)
24. 24.What is the distance between the points (4, 2) and (16, 11)? (a) 16 (b) 15 (c) 225 (d) 21
25. 25.In which quadrant does the point (8, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
26. 26.What is the distance between the points (9, 1) and (13, 4)? (a) 5 (b) 7 (c) 6 (d) 25
27. 27.What is the distance between the points (1, 21) and (17, 9)? (a) 400 (b) 28 (c) 20 (d) 21
28. 28.In which quadrant does the point (−6, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
30. 30.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
31. 31.What is the midpoint of the line joining (7, 12) and (19, 4)? (a) (8, 13) (b) (13, 8) (c) (6, 4) (d) (26, 16)
32. 32.What is the midpoint of the line joining (10, 1) and (14, 9)? (a) (2, 4) (b) (12, 5) (c) (24, 10) (d) (5, 12)
33. 33.What is the distance between the points (6, 8) and (18, 3)? (a) 17 (b) 169 (c) 13 (d) 14
34. 34.In which quadrant does the point (9, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
35. 35.What is the midpoint of the line joining (1, 18) and (3, 8)? (a) (2, 13) (b) (4, 26) (c) (13, 2) (d) (1, 5)
36. 36.In which quadrant does the point (−9, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
37. 37.What is the midpoint of the line joining (7, 1) and (11, 5)? (a) (2, 2) (b) (3, 9) (c) (9, 3) (d) (18, 6)
38. 38.What is the distance between the points (0, 0) and (4, 3)? (a) 6 (b) 5 (c) 7 (d) 25
39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
40. 40.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant

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