Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 508 · 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 (3, 1) and (9, 7)? (a) (12, 8) (b) (6, 4) (c) (3, 3) (d) (4, 6)
2. 2.In which quadrant does the point (−5, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
4. 4.What is the distance between the points (5, 19) and (10, 7)? (a) 17 (b) 13 (c) 14 (d) 169
5. 5.What is the midpoint of the line joining (7, 8) and (11, 6)? (a) (7, 9) (b) (2, 1) (c) (9, 7) (d) (18, 14)
6. 6.What is the distance between the points (9, 13) and (33, 6)? (a) 26 (b) 625 (c) 25 (d) 31
7. 7.What is the distance between the points (1, 8) and (5, 11)? (a) 6 (b) 7 (c) 5 (d) 25
8. 8.What is the distance between the points (2, 16) and (14, 0)? (a) 28 (b) 400 (c) 20 (d) 21
9. 9.What is the midpoint of the line joining (10, 17) and (12, 9)? (a) (22, 26) (b) (1, 4) (c) (13, 11) (d) (11, 13)
10. 10.What is the distance between the points (8, 8) and (32, 15)? (a) 625 (b) 31 (c) 25 (d) 26
11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
12. 12.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
15. 15.In which quadrant does the point (3, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
16. 16.What is the distance between the points (9, 0) and (17, 6)? (a) 14 (b) 100 (c) 11 (d) 10
17. 17.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
18. 18.In which quadrant does the point (−8, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
20. 20.What is the distance between the points (5, 1) and (8, 5)? (a) 25 (b) 6 (c) 7 (d) 5
21. 21.What is the midpoint of the line joining (10, 6) and (16, 2)? (a) (4, 13) (b) (13, 4) (c) (3, 2) (d) (26, 8)
22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
23. 23.What is the distance between the points (8, 7) and (12, 10)? (a) 6 (b) 25 (c) 5 (d) 7
24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
26. 26.What is the distance between the points (5, 9) and (10, 21)? (a) 17 (b) 13 (c) 14 (d) 169
27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
28. 28.What is the distance between the points (5, 8) and (17, 3)? (a) 169 (b) 14 (c) 17 (d) 13
29. 29.In which quadrant does the point (−5, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
30. 30.What is the distance between the points (7, 16) and (19, 7)? (a) 21 (b) 16 (c) 15 (d) 225
31. 31.What is the midpoint of the line joining (6, 8) and (8, 10)? (a) (1, 1) (b) (14, 18) (c) (7, 9) (d) (9, 7)
32. 32.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
33. 33.What is the distance between the points (7, 3) and (19, 19)? (a) 400 (b) 20 (c) 21 (d) 28
34. 34.What is the midpoint of the line joining (0, 4) and (8, 2)? (a) (4, 1) (b) (3, 4) (c) (8, 6) (d) (4, 3)
35. 35.In which quadrant does the point (−3, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
36. 36.What is the midpoint of the line joining (1, 9) and (3, 7)? (a) (1, 1) (b) (8, 2) (c) (4, 16) (d) (2, 8)
37. 37.What is the midpoint of the line joining (8, 6) and (14, 4)? (a) (22, 10) (b) (11, 5) (c) (5, 11) (d) (3, 1)
38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
39. 39.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
40. 40.In which quadrant does the point (2, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant

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