Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 771 · 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.In which quadrant does the point (−1, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
2. 2.What is the distance between the points (0, 18) and (9, 6)? (a) 225 (b) 16 (c) 15 (d) 21
3. 3.What is the midpoint of the line joining (3, 9) and (9, 13)? (a) (6, 11) (b) (3, 2) (c) (11, 6) (d) (12, 22)
4. 4.What is the midpoint of the line joining (9, 13) and (15, 7)? (a) (24, 20) (b) (10, 12) (c) (3, 3) (d) (12, 10)
5. 5.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
6. 6.In which quadrant does the point (−6, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
7. 7.What is the distance between the points (5, 4) and (14, 16)? (a) 21 (b) 16 (c) 225 (d) 15
8. 8.What is the distance between the points (0, 18) and (12, 2)? (a) 28 (b) 20 (c) 21 (d) 400
9. 9.What is the midpoint of the line joining (1, 14) and (7, 4)? (a) (4, 9) (b) (9, 4) (c) (3, 5) (d) (8, 18)
10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
11. 11.What is the distance between the points (5, 24) and (13, 9)? (a) 17 (b) 18 (c) 23 (d) 289
12. 12.What is the distance between the points (3, 10) and (6, 6)? (a) 7 (b) 6 (c) 5 (d) 25
13. 13.What is the midpoint of the line joining (8, 7) and (10, 15)? (a) (11, 9) (b) (18, 22) (c) (1, 4) (d) (9, 11)
14. 14.In which quadrant does the point (−8, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
15. 15.What is the distance between the points (8, 21) and (13, 9)? (a) 17 (b) 13 (c) 169 (d) 14
16. 16.What is the midpoint of the line joining (10, 8) and (18, 18)? (a) (4, 5) (b) (13, 14) (c) (14, 13) (d) (28, 26)
17. 17.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
18. 18.What is the distance between the points (8, 0) and (11, 4)? (a) 6 (b) 5 (c) 7 (d) 25
19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
20. 20.What is the distance between the points (6, 8) and (18, 3)? (a) 13 (b) 14 (c) 17 (d) 169
21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
22. 22.What is the midpoint of the line joining (1, 15) and (11, 9)? (a) (12, 24) (b) (5, 3) (c) (6, 12) (d) (12, 6)
23. 23.What is the distance between the points (1, 9) and (16, 17)? (a) 18 (b) 17 (c) 289 (d) 23
24. 24.What is the midpoint of the line joining (6, 7) and (12, 17)? (a) (9, 12) (b) (12, 9) (c) (18, 24) (d) (3, 5)
25. 25.In which quadrant does the point (−7, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
26. 26.What is the midpoint of the line joining (1, 11) and (9, 7)? (a) (9, 5) (b) (10, 18) (c) (4, 2) (d) (5, 9)
27. 27.What is the midpoint of the line joining (10, 2) and (14, 6)? (a) (2, 2) (b) (24, 8) (c) (4, 12) (d) (12, 4)
28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
29. 29.What is the midpoint of the line joining (10, 6) and (12, 10)? (a) (1, 2) (b) (22, 16) (c) (8, 11) (d) (11, 8)
30. 30.What is the distance between the points (9, 9) and (21, 0)? (a) 16 (b) 15 (c) 225 (d) 21
31. 31.In which quadrant does the point (4, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
33. 33.What is the midpoint of the line joining (2, 1) and (14, 11)? (a) (6, 5) (b) (16, 12) (c) (8, 6) (d) (6, 8)
34. 34.In which quadrant does the point (9, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
35. 35.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
36. 36.What is the midpoint of the line joining (8, 5) and (14, 11)? (a) (3, 3) (b) (11, 8) (c) (8, 11) (d) (22, 16)
37. 37.What is the midpoint of the line joining (7, 9) and (9, 13)? (a) (11, 8) (b) (1, 2) (c) (16, 22) (d) (8, 11)
38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
39. 39.What is the midpoint of the line joining (1, 0) and (9, 12)? (a) (6, 5) (b) (10, 12) (c) (5, 6) (d) (4, 6)
40. 40.In which quadrant does the point (−5, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant

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