Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 113 · 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, 6) and (16, 8)? (a) (10, 7) (b) (6, 1) (c) (7, 10) (d) (20, 14)
2. 2.In which quadrant does the point (9, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
3. 3.In which quadrant does the point (1, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
4. 4.What is the distance between the points (5, 6) and (9, 9)? (a) 7 (b) 6 (c) 5 (d) 25
5. 5.What is the midpoint of the line joining (2, 0) and (6, 2)? (a) (8, 2) (b) (2, 1) (c) (1, 4) (d) (4, 1)
6. 6.What is the distance between the points (6, 0) and (15, 12)? (a) 16 (b) 21 (c) 225 (d) 15
7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
9. 9.In which quadrant does the point (3, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
10. 10.What is the distance between the points (0, 12) and (12, 7)? (a) 13 (b) 17 (c) 14 (d) 169
11. 11.What is the midpoint of the line joining (5, 14) and (7, 2)? (a) (6, 8) (b) (12, 16) (c) (1, 6) (d) (8, 6)
12. 12.In which quadrant does the point (−4, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
13. 13.In which quadrant does the point (3, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
14. 14.In which quadrant does the point (7, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
15. 15.What is the distance between the points (1, 16) and (13, 0)? (a) 20 (b) 21 (c) 28 (d) 400
16. 16.In which quadrant does the point (6, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
17. 17.What is the midpoint of the line joining (8, 17) and (20, 9)? (a) (13, 14) (b) (28, 26) (c) (6, 4) (d) (14, 13)
18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
19. 19.What is the distance between the points (6, 20) and (18, 4)? (a) 28 (b) 21 (c) 400 (d) 20
20. 20.What is the midpoint of the line joining (5, 6) and (15, 10)? (a) (10, 8) (b) (8, 10) (c) (5, 2) (d) (20, 16)
21. 21.In which quadrant does the point (−7, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
23. 23.In which quadrant does the point (−5, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
24. 24.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
26. 26.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
27. 27.In which quadrant does the point (9, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the distance between the points (4, 20) and (13, 8)? (a) 16 (b) 225 (c) 21 (d) 15
29. 29.What is the midpoint of the line joining (8, 3) and (14, 5)? (a) (22, 8) (b) (3, 1) (c) (11, 4) (d) (4, 11)
30. 30.In which quadrant does the point (−3, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
31. 31.What is the midpoint of the line joining (1, 11) and (9, 1)? (a) (10, 12) (b) (4, 5) (c) (6, 5) (d) (5, 6)
32. 32.What is the midpoint of the line joining (5, 0) and (9, 4)? (a) (2, 2) (b) (14, 4) (c) (2, 7) (d) (7, 2)
33. 33.In which quadrant does the point (6, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
34. 34.What is the distance between the points (4, 7) and (28, 14)? (a) 31 (b) 26 (c) 625 (d) 25
35. 35.In which quadrant does the point (−9, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
36. 36.In which quadrant does the point (−9, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
37. 37.What is the midpoint of the line joining (10, 16) and (18, 8)? (a) (28, 24) (b) (14, 12) (c) (12, 14) (d) (4, 4)
38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
39. 39.What is the midpoint of the line joining (3, 8) and (13, 2)? (a) (16, 10) (b) (8, 5) (c) (5, 8) (d) (5, 3)
40. 40.What is the distance between the points (1, 0) and (8, 24)? (a) 26 (b) 31 (c) 25 (d) 625

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