Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 946 · 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, 10) and (15, 2)? (a) (24, 12) (b) (12, 6) (c) (3, 4) (d) (6, 12)
2. 2.What is the distance between the points (9, 15) and (17, 9)? (a) 100 (b) 14 (c) 11 (d) 10
3. 3.In which quadrant does the point (−7, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
5. 5.What is the distance between the points (9, 0) and (17, 6)? (a) 14 (b) 10 (c) 11 (d) 100
6. 6.What is the midpoint of the line joining (10, 19) and (18, 9)? (a) (28, 28) (b) (4, 5) (c) (15, 14) (d) (14, 14)
7. 7.What is the distance between the points (0, 14) and (12, 9)? (a) 169 (b) 14 (c) 17 (d) 13
8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
9. 9.What is the distance between the points (8, 16) and (14, 8)? (a) 10 (b) 100 (c) 14 (d) 11
10. 10.In which quadrant does the point (−1, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
11. 11.What is the midpoint of the line joining (5, 9) and (11, 19)? (a) (8, 14) (b) (14, 8) (c) (3, 5) (d) (16, 28)
12. 12.In which quadrant does the point (−1, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
13. 13.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
14. 14.What is the midpoint of the line joining (10, 4) and (12, 10)? (a) (1, 3) (b) (7, 11) (c) (11, 7) (d) (22, 14)
15. 15.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
16. 16.What is the midpoint of the line joining (7, 2) and (13, 8)? (a) (5, 10) (b) (3, 3) (c) (10, 5) (d) (20, 10)
17. 17.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
18. 18.In which quadrant does the point (1, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
20. 20.In which quadrant does the point (−3, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
22. 22.What is the midpoint of the line joining (1, 7) and (13, 1)? (a) (6, 3) (b) (14, 8) (c) (4, 7) (d) (7, 4)
23. 23.In which quadrant does the point (−7, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
24. 24.What is the distance between the points (4, 14) and (16, 5)? (a) 21 (b) 225 (c) 15 (d) 16
25. 25.What is the midpoint of the line joining (8, 12) and (18, 4)? (a) (26, 16) (b) (8, 13) (c) (5, 4) (d) (13, 8)
26. 26.What is the midpoint of the line joining (10, 3) and (12, 1)? (a) (2, 11) (b) (1, 1) (c) (11, 2) (d) (22, 4)
27. 27.What is the midpoint of the line joining (4, 4) and (12, 6)? (a) (4, 1) (b) (5, 8) (c) (16, 10) (d) (8, 5)
28. 28.In which quadrant does the point (4, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
29. 29.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
30. 30.In which quadrant does the point (8, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
31. 31.In which quadrant does the point (−7, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
33. 33.What is the midpoint of the line joining (6, 5) and (10, 3)? (a) (2, 1) (b) (4, 8) (c) (8, 4) (d) (16, 8)
34. 34.What is the distance between the points (1, 32) and (8, 8)? (a) 31 (b) 26 (c) 625 (d) 25
35. 35.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
36. 36.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.What is the midpoint of the line joining (8, 6) and (14, 10)? (a) (3, 2) (b) (11, 8) (c) (8, 11) (d) (22, 16)
38. 38.What is the midpoint of the line joining (0, 1) and (6, 3)? (a) (3, 1) (b) (2, 3) (c) (6, 4) (d) (3, 2)
39. 39.What is the distance between the points (1, 1) and (6, 13)? (a) 14 (b) 17 (c) 169 (d) 13
40. 40.What is the midpoint of the line joining (10, 10) and (20, 2)? (a) (30, 12) (b) (5, 4) (c) (6, 15) (d) (15, 6)

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