Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 129 · 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, 10) and (18, 20)? (a) (15, 13) (b) (13, 15) (c) (26, 30) (d) (5, 5)
2. 2.What is the midpoint of the line joining (9, 4) and (21, 2)? (a) (30, 6) (b) (6, 1) (c) (3, 15) (d) (15, 3)
3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
4. 4.In which quadrant does the point (−4, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
5. 5.What is the midpoint of the line joining (2, 18) and (12, 8)? (a) (13, 7) (b) (14, 26) (c) (5, 5) (d) (7, 13)
6. 6.What is the midpoint of the line joining (3, 21) and (9, 9)? (a) (3, 6) (b) (6, 15) (c) (12, 30) (d) (15, 6)
7. 7.What is the distance between the points (2, 9) and (14, 0)? (a) 16 (b) 225 (c) 15 (d) 21
8. 8.In which quadrant does the point (6, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
9. 9.In which quadrant does the point (7, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
10. 10.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
11. 11.What is the midpoint of the line joining (3, 17) and (9, 5)? (a) (6, 11) (b) (11, 6) (c) (3, 6) (d) (12, 22)
12. 12.What is the midpoint of the line joining (4, 7) and (16, 9)? (a) (8, 10) (b) (20, 16) (c) (10, 8) (d) (6, 1)
13. 13.What is the distance between the points (5, 11) and (8, 7)? (a) 6 (b) 25 (c) 5 (d) 7
14. 14.What is the distance between the points (1, 18) and (10, 6)? (a) 21 (b) 16 (c) 15 (d) 225
15. 15.In which quadrant does the point (4, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (6, 4) and (12, 2)? (a) (18, 6) (b) (9, 3) (c) (3, 1) (d) (3, 9)
17. 17.In which quadrant does the point (−6, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
18. 18.What is the distance between the points (2, 7) and (26, 0)? (a) 26 (b) 31 (c) 25 (d) 625
19. 19.What is the midpoint of the line joining (9, 0) and (19, 6)? (a) (3, 14) (b) (28, 6) (c) (5, 3) (d) (14, 3)
20. 20.In which quadrant does the point (9, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
21. 21.In which quadrant does the point (−8, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
22. 22.What is the distance between the points (2, 3) and (11, 15)? (a) 225 (b) 21 (c) 15 (d) 16
23. 23.In which quadrant does the point (4, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
26. 26.What is the midpoint of the line joining (7, 10) and (11, 2)? (a) (6, 9) (b) (18, 12) (c) (9, 6) (d) (2, 4)
27. 27.What is the midpoint of the line joining (6, 10) and (12, 12)? (a) (3, 1) (b) (18, 22) (c) (11, 9) (d) (9, 11)
28. 28.What is the midpoint of the line joining (9, 11) and (19, 3)? (a) (5, 4) (b) (14, 7) (c) (7, 14) (d) (28, 14)
29. 29.In which quadrant does the point (5, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
30. 30.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
31. 31.What is the midpoint of the line joining (0, 18) and (2, 6)? (a) (1, 6) (b) (2, 24) (c) (12, 1) (d) (1, 12)
32. 32.What is the midpoint of the line joining (3, 0) and (9, 10)? (a) (3, 5) (b) (6, 5) (c) (12, 10) (d) (5, 6)
33. 33.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
34. 34.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
35. 35.In which quadrant does the point (7, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
36. 36.What is the midpoint of the line joining (8, 7) and (12, 13)? (a) (2, 3) (b) (20, 20) (c) (10, 10) (d) (11, 10)
37. 37.What is the midpoint of the line joining (1, 10) and (5, 4)? (a) (3, 7) (b) (7, 3) (c) (2, 3) (d) (6, 14)
38. 38.What is the distance between the points (8, 4) and (32, 11)? (a) 625 (b) 31 (c) 26 (d) 25
39. 39.What is the distance between the points (7, 5) and (19, 10)? (a) 14 (b) 169 (c) 13 (d) 17
40. 40.What is the distance between the points (4, 5) and (16, 14)? (a) 225 (b) 15 (c) 16 (d) 21

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