Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 154 · 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 (9, 3) and (21, 15)? (a) (6, 6) (b) (9, 15) (c) (30, 18) (d) (15, 9)
2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
3. 3.What is the midpoint of the line joining (7, 10) and (17, 4)? (a) (12, 7) (b) (24, 14) (c) (7, 12) (d) (5, 3)
4. 4.What is the distance between the points (8, 2) and (32, 9)? (a) 25 (b) 31 (c) 625 (d) 26
5. 5.What is the distance between the points (9, 16) and (21, 0)? (a) 28 (b) 400 (c) 21 (d) 20
6. 6.What is the distance between the points (9, 18) and (14, 6)? (a) 14 (b) 169 (c) 17 (d) 13
7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
8. 8.What is the distance between the points (8, 1) and (20, 10)? (a) 225 (b) 16 (c) 21 (d) 15
9. 9.In which quadrant does the point (−5, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
11. 11.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
12. 12.What is the midpoint of the line joining (7, 8) and (15, 20)? (a) (22, 28) (b) (4, 6) (c) (14, 11) (d) (11, 14)
13. 13.What is the distance between the points (1, 13) and (9, 7)? (a) 100 (b) 14 (c) 11 (d) 10
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
15. 15.What is the midpoint of the line joining (5, 5) and (9, 15)? (a) (7, 10) (b) (14, 20) (c) (2, 5) (d) (10, 7)
16. 16.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
17. 17.In which quadrant does the point (8, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
18. 18.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
19. 19.In which quadrant does the point (5, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
20. 20.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
21. 21.What is the midpoint of the line joining (7, 5) and (19, 7)? (a) (6, 1) (b) (26, 12) (c) (6, 13) (d) (13, 6)
22. 22.What is the midpoint of the line joining (10, 9) and (18, 1)? (a) (28, 10) (b) (14, 5) (c) (4, 4) (d) (5, 14)
23. 23.What is the distance between the points (0, 16) and (24, 9)? (a) 31 (b) 26 (c) 625 (d) 25
24. 24.In which quadrant does the point (−9, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
25. 25.What is the midpoint of the line joining (8, 5) and (10, 7)? (a) (1, 1) (b) (6, 9) (c) (9, 6) (d) (18, 12)
26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
27. 27.What is the distance between the points (5, 3) and (10, 15)? (a) 169 (b) 14 (c) 13 (d) 17
28. 28.What is the midpoint of the line joining (10, 9) and (16, 15)? (a) (12, 13) (b) (13, 12) (c) (26, 24) (d) (3, 3)
29. 29.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
30. 30.What is the distance between the points (6, 9) and (30, 16)? (a) 625 (b) 25 (c) 31 (d) 26
31. 31.What is the distance between the points (2, 23) and (10, 8)? (a) 289 (b) 18 (c) 17 (d) 23
32. 32.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
33. 33.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
34. 34.What is the distance between the points (0, 2) and (24, 9)? (a) 625 (b) 26 (c) 25 (d) 31
35. 35.In which quadrant does the point (9, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
36. 36.What is the midpoint of the line joining (7, 12) and (19, 6)? (a) (26, 18) (b) (6, 3) (c) (9, 13) (d) (13, 9)
37. 37.In which quadrant does the point (2, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
38. 38.What is the distance between the points (6, 3) and (12, 11)? (a) 11 (b) 100 (c) 14 (d) 10
39. 39.What is the distance between the points (0, 7) and (12, 16)? (a) 15 (b) 21 (c) 16 (d) 225
40. 40.What is the midpoint of the line joining (2, 4) and (14, 14)? (a) (8, 9) (b) (16, 18) (c) (9, 8) (d) (6, 5)

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