Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 153 · 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 (2, 9) and (10, 7)? (a) (12, 16) (b) (4, 1) (c) (6, 8) (d) (8, 6)
2. 2.What is the distance between the points (3, 12) and (8, 0)? (a) 169 (b) 14 (c) 13 (d) 17
3. 3.What is the midpoint of the line joining (1, 3) and (5, 15)? (a) (6, 18) (b) (3, 9) (c) (2, 6) (d) (9, 3)
4. 4.What is the midpoint of the line joining (7, 10) and (9, 8)? (a) (16, 18) (b) (9, 8) (c) (1, 1) (d) (8, 9)
5. 5.What is the distance between the points (0, 23) and (12, 7)? (a) 20 (b) 21 (c) 400 (d) 28
6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
7. 7.What is the midpoint of the line joining (8, 4) and (18, 10)? (a) (5, 3) (b) (7, 13) (c) (26, 14) (d) (13, 7)
8. 8.What is the midpoint of the line joining (10, 15) and (12, 7)? (a) (1, 4) (b) (22, 22) (c) (12, 11) (d) (11, 11)
9. 9.In which quadrant does the point (1, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
11. 11.What is the midpoint of the line joining (4, 9) and (10, 1)? (a) (14, 10) (b) (7, 5) (c) (3, 4) (d) (5, 7)
12. 12.What is the distance between the points (5, 25) and (17, 9)? (a) 21 (b) 28 (c) 20 (d) 400
13. 13.What is the distance between the points (4, 21) and (16, 5)? (a) 21 (b) 20 (c) 400 (d) 28
14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
15. 15.What is the distance between the points (4, 0) and (7, 4)? (a) 25 (b) 5 (c) 6 (d) 7
16. 16.What is the midpoint of the line joining (6, 8) and (14, 20)? (a) (20, 28) (b) (10, 14) (c) (14, 10) (d) (4, 6)
17. 17.What is the midpoint of the line joining (4, 6) and (6, 18)? (a) (5, 12) (b) (10, 24) (c) (1, 6) (d) (12, 5)
18. 18.In which quadrant does the point (4, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
19. 19.What is the distance between the points (0, 16) and (8, 1)? (a) 289 (b) 23 (c) 17 (d) 18
20. 20.In which quadrant does the point (−4, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
21. 21.What is the distance between the points (5, 7) and (29, 0)? (a) 25 (b) 31 (c) 26 (d) 625
22. 22.What is the distance between the points (9, 17) and (17, 2)? (a) 289 (b) 18 (c) 23 (d) 17
23. 23.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
24. 24.What is the midpoint of the line joining (2, 6) and (4, 4)? (a) (1, 1) (b) (5, 3) (c) (3, 5) (d) (6, 10)
25. 25.What is the distance between the points (7, 9) and (19, 4)? (a) 14 (b) 17 (c) 169 (d) 13
26. 26.In which quadrant does the point (3, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
27. 27.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
28. 28.In which quadrant does the point (−2, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
29. 29.In which quadrant does the point (−9, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
30. 30.In which quadrant does the point (−6, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
31. 31.In which quadrant does the point (−7, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
32. 32.What is the distance between the points (9, 0) and (17, 15)? (a) 17 (b) 23 (c) 289 (d) 18
33. 33.In which quadrant does the point (−2, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
34. 34.What is the midpoint of the line joining (9, 18) and (11, 6)? (a) (1, 6) (b) (20, 24) (c) (12, 10) (d) (10, 12)
35. 35.What is the distance between the points (9, 3) and (13, 6)? (a) 7 (b) 5 (c) 6 (d) 25
36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
38. 38.What is the midpoint of the line joining (5, 1) and (9, 9)? (a) (2, 4) (b) (14, 10) (c) (7, 5) (d) (5, 7)
39. 39.What is the midpoint of the line joining (9, 5) and (11, 9)? (a) (7, 10) (b) (20, 14) (c) (1, 2) (d) (10, 7)
40. 40.What is the distance between the points (7, 16) and (23, 4)? (a) 21 (b) 28 (c) 400 (d) 20

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