Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 83 · 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 (4, 15) and (8, 3)? (a) (9, 6) (b) (2, 6) (c) (12, 18) (d) (6, 9)
2. 2.In which quadrant does the point (−3, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
3. 3.What is the distance between the points (9, 7) and (15, 15)? (a) 14 (b) 11 (c) 100 (d) 10
4. 4.In which quadrant does the point (9, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
6. 6.What is the midpoint of the line joining (5, 10) and (13, 16)? (a) (4, 3) (b) (18, 26) (c) (9, 13) (d) (13, 9)
7. 7.In which quadrant does the point (−1, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
8. 8.What is the distance between the points (2, 9) and (14, 18)? (a) 21 (b) 15 (c) 16 (d) 225
9. 9.What is the midpoint of the line joining (6, 13) and (18, 5)? (a) (6, 4) (b) (24, 18) (c) (12, 9) (d) (9, 12)
10. 10.What is the midpoint of the line joining (4, 8) and (16, 16)? (a) (20, 24) (b) (12, 10) (c) (10, 12) (d) (6, 4)
11. 11.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
12. 12.What is the midpoint of the line joining (4, 8) and (6, 12)? (a) (5, 10) (b) (10, 20) (c) (1, 2) (d) (10, 5)
13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
14. 14.What is the midpoint of the line joining (5, 10) and (7, 12)? (a) (6, 11) (b) (12, 22) (c) (1, 1) (d) (11, 6)
15. 15.What is the distance between the points (2, 7) and (6, 10)? (a) 6 (b) 5 (c) 7 (d) 25
16. 16.In which quadrant does the point (3, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
17. 17.What is the midpoint of the line joining (2, 3) and (14, 15)? (a) (8, 9) (b) (9, 8) (c) (16, 18) (d) (6, 6)
18. 18.What is the distance between the points (3, 3) and (15, 19)? (a) 21 (b) 20 (c) 28 (d) 400
19. 19.In which quadrant does the point (7, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
21. 21.What is the midpoint of the line joining (3, 2) and (5, 0)? (a) (4, 1) (b) (1, 4) (c) (8, 2) (d) (1, 1)
22. 22.What is the midpoint of the line joining (1, 4) and (5, 10)? (a) (2, 3) (b) (7, 3) (c) (6, 14) (d) (3, 7)
23. 23.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
24. 24.What is the midpoint of the line joining (5, 0) and (7, 2)? (a) (12, 2) (b) (6, 1) (c) (1, 6) (d) (1, 1)
25. 25.In which quadrant does the point (8, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
26. 26.What is the distance between the points (0, 4) and (15, 12)? (a) 18 (b) 23 (c) 289 (d) 17
27. 27.What is the midpoint of the line joining (5, 2) and (17, 8)? (a) (5, 11) (b) (11, 5) (c) (22, 10) (d) (6, 3)
28. 28.In which quadrant does the point (9, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
29. 29.In which quadrant does the point (−7, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
30. 30.What is the midpoint of the line joining (3, 8) and (9, 2)? (a) (3, 3) (b) (6, 5) (c) (5, 6) (d) (12, 10)
31. 31.What is the distance between the points (9, 0) and (21, 5)? (a) 169 (b) 17 (c) 13 (d) 14
32. 32.What is the distance between the points (1, 6) and (13, 22)? (a) 21 (b) 28 (c) 20 (d) 400
33. 33.What is the distance between the points (7, 2) and (16, 14)? (a) 16 (b) 225 (c) 15 (d) 21
34. 34.What is the distance between the points (0, 21) and (5, 9)? (a) 17 (b) 14 (c) 13 (d) 169
35. 35.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
36. 36.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
37. 37.What is the distance between the points (0, 1) and (8, 16)? (a) 18 (b) 289 (c) 17 (d) 23
38. 38.In which quadrant does the point (−7, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
40. 40.What is the distance between the points (2, 24) and (9, 0)? (a) 31 (b) 26 (c) 25 (d) 625

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