Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 852 · 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 distance between the points (9, 16) and (21, 0)? (a) 28 (b) 21 (c) 20 (d) 400
2. 2.In which quadrant does the point (−2, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
3. 3.What is the distance between the points (5, 2) and (12, 26)? (a) 31 (b) 625 (c) 25 (d) 26
4. 4.What is the distance between the points (7, 0) and (31, 7)? (a) 25 (b) 26 (c) 625 (d) 31
5. 5.What is the midpoint of the line joining (4, 15) and (14, 7)? (a) (18, 22) (b) (5, 4) (c) (11, 9) (d) (9, 11)
6. 6.What is the distance between the points (9, 33) and (16, 9)? (a) 31 (b) 26 (c) 625 (d) 25
7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
8. 8.What is the midpoint of the line joining (1, 14) and (7, 10)? (a) (3, 2) (b) (4, 12) (c) (12, 4) (d) (8, 24)
9. 9.What is the midpoint of the line joining (3, 1) and (9, 7)? (a) (6, 4) (b) (4, 6) (c) (3, 3) (d) (12, 8)
10. 10.What is the midpoint of the line joining (7, 1) and (15, 5)? (a) (11, 3) (b) (3, 11) (c) (4, 2) (d) (22, 6)
11. 11.What is the midpoint of the line joining (4, 5) and (14, 11)? (a) (9, 8) (b) (18, 16) (c) (8, 9) (d) (5, 3)
12. 12.What is the distance between the points (7, 21) and (12, 9)? (a) 17 (b) 13 (c) 169 (d) 14
13. 13.What is the distance between the points (9, 1) and (21, 6)? (a) 14 (b) 13 (c) 169 (d) 17
14. 14.What is the midpoint of the line joining (3, 11) and (13, 5)? (a) (8, 8) (b) (16, 16) (c) (9, 8) (d) (5, 3)
15. 15.What is the distance between the points (1, 26) and (8, 2)? (a) 25 (b) 31 (c) 625 (d) 26
16. 16.In which quadrant does the point (8, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
17. 17.What is the midpoint of the line joining (3, 5) and (7, 3)? (a) (10, 8) (b) (4, 5) (c) (5, 4) (d) (2, 1)
18. 18.What is the distance between the points (2, 2) and (17, 10)? (a) 17 (b) 18 (c) 23 (d) 289
19. 19.What is the distance between the points (2, 19) and (14, 3)? (a) 28 (b) 400 (c) 20 (d) 21
20. 20.What is the distance between the points (1, 18) and (17, 6)? (a) 20 (b) 400 (c) 21 (d) 28
21. 21.What is the midpoint of the line joining (6, 22) and (12, 10)? (a) (16, 9) (b) (9, 16) (c) (18, 32) (d) (3, 6)
22. 22.What is the distance between the points (7, 25) and (19, 9)? (a) 21 (b) 400 (c) 28 (d) 20
23. 23.What is the distance between the points (2, 7) and (9, 31)? (a) 31 (b) 26 (c) 25 (d) 625
24. 24.In which quadrant does the point (2, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
25. 25.In which quadrant does the point (6, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
26. 26.In which quadrant does the point (−8, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
29. 29.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
30. 30.What is the midpoint of the line joining (5, 2) and (7, 12)? (a) (1, 5) (b) (6, 7) (c) (7, 6) (d) (12, 14)
31. 31.What is the midpoint of the line joining (8, 9) and (14, 5)? (a) (11, 7) (b) (7, 11) (c) (3, 2) (d) (22, 14)
32. 32.What is the midpoint of the line joining (10, 0) and (12, 6)? (a) (11, 3) (b) (1, 3) (c) (22, 6) (d) (3, 11)
33. 33.What is the distance between the points (6, 7) and (10, 10)? (a) 6 (b) 5 (c) 25 (d) 7
34. 34.In which quadrant does the point (2, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
36. 36.In which quadrant does the point (5, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
37. 37.What is the distance between the points (9, 9) and (21, 0)? (a) 21 (b) 15 (c) 225 (d) 16
38. 38.In which quadrant does the point (−3, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
39. 39.What is the distance between the points (5, 12) and (21, 0)? (a) 20 (b) 21 (c) 400 (d) 28
40. 40.What is the midpoint of the line joining (7, 8) and (11, 20)? (a) (14, 9) (b) (18, 28) (c) (2, 6) (d) (9, 14)

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