Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 185 · 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 (1, 8) and (9, 12)? (a) (10, 20) (b) (10, 5) (c) (4, 2) (d) (5, 10)
2. 2.In which quadrant does the point (5, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
4. 4.What is the distance between the points (8, 16) and (14, 8)? (a) 14 (b) 100 (c) 10 (d) 11
5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
7. 7.What is the distance between the points (2, 25) and (9, 1)? (a) 625 (b) 25 (c) 26 (d) 31
8. 8.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.In which quadrant does the point (8, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
10. 10.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
12. 12.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
15. 15.What is the distance between the points (9, 18) and (21, 2)? (a) 21 (b) 400 (c) 28 (d) 20
16. 16.What is the midpoint of the line joining (7, 0) and (13, 4)? (a) (10, 2) (b) (2, 10) (c) (20, 4) (d) (3, 2)
17. 17.In which quadrant does the point (4, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
18. 18.In which quadrant does the point (−8, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
19. 19.What is the distance between the points (5, 8) and (11, 0)? (a) 11 (b) 14 (c) 10 (d) 100
20. 20.What is the midpoint of the line joining (2, 5) and (12, 9)? (a) (8, 7) (b) (5, 2) (c) (7, 7) (d) (14, 14)
21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
22. 22.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
23. 23.In which quadrant does the point (−5, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
24. 24.What is the midpoint of the line joining (0, 13) and (2, 3)? (a) (2, 16) (b) (1, 8) (c) (1, 5) (d) (8, 1)
25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
26. 26.In which quadrant does the point (−2, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
27. 27.What is the midpoint of the line joining (9, 16) and (11, 10)? (a) (20, 26) (b) (1, 3) (c) (13, 10) (d) (10, 13)
28. 28.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
29. 29.What is the distance between the points (7, 4) and (15, 10)? (a) 11 (b) 100 (c) 14 (d) 10
30. 30.In which quadrant does the point (4, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
31. 31.What is the distance between the points (7, 14) and (19, 9)? (a) 169 (b) 17 (c) 14 (d) 13
32. 32.What is the midpoint of the line joining (10, 3) and (14, 1)? (a) (2, 1) (b) (2, 12) (c) (12, 2) (d) (24, 4)
33. 33.What is the midpoint of the line joining (10, 8) and (18, 12)? (a) (10, 14) (b) (4, 2) (c) (28, 20) (d) (14, 10)
34. 34.What is the distance between the points (6, 16) and (14, 1)? (a) 23 (b) 289 (c) 17 (d) 18
35. 35.What is the midpoint of the line joining (6, 17) and (8, 9)? (a) (13, 7) (b) (1, 4) (c) (14, 26) (d) (7, 13)
36. 36.In which quadrant does the point (−5, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
37. 37.What is the midpoint of the line joining (1, 11) and (13, 7)? (a) (7, 9) (b) (6, 2) (c) (9, 7) (d) (14, 18)
38. 38.What is the distance between the points (0, 7) and (16, 19)? (a) 21 (b) 400 (c) 28 (d) 20
39. 39.In which quadrant does the point (−1, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
40. 40.What is the midpoint of the line joining (9, 7) and (21, 15)? (a) (6, 4) (b) (15, 11) (c) (11, 15) (d) (30, 22)

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