Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 230 · 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 distance between the points (0, 9) and (24, 2)? (a) 26 (b) 625 (c) 25 (d) 31
2. 2.What is the distance between the points (5, 7) and (9, 10)? (a) 25 (b) 7 (c) 6 (d) 5
3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
4. 4.What is the distance between the points (6, 2) and (15, 14)? (a) 225 (b) 21 (c) 15 (d) 16
5. 5.What is the distance between the points (0, 3) and (12, 8)? (a) 17 (b) 13 (c) 169 (d) 14
6. 6.In which quadrant does the point (9, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
8. 8.In which quadrant does the point (9, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
9. 9.What is the distance between the points (7, 2) and (19, 7)? (a) 17 (b) 14 (c) 169 (d) 13
10. 10.What is the midpoint of the line joining (0, 11) and (4, 5)? (a) (2, 3) (b) (2, 8) (c) (4, 16) (d) (8, 2)
11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
12. 12.What is the midpoint of the line joining (7, 4) and (19, 0)? (a) (6, 2) (b) (13, 2) (c) (26, 4) (d) (2, 13)
13. 13.What is the midpoint of the line joining (9, 2) and (13, 4)? (a) (22, 6) (b) (3, 11) (c) (2, 1) (d) (11, 3)
14. 14.What is the midpoint of the line joining (1, 4) and (9, 8)? (a) (10, 12) (b) (5, 6) (c) (6, 5) (d) (4, 2)
15. 15.What is the midpoint of the line joining (8, 2) and (14, 8)? (a) (5, 11) (b) (3, 3) (c) (11, 5) (d) (22, 10)
16. 16.What is the midpoint of the line joining (1, 7) and (9, 19)? (a) (10, 26) (b) (13, 5) (c) (5, 13) (d) (4, 6)
17. 17.In which quadrant does the point (3, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
18. 18.What is the midpoint of the line joining (6, 3) and (10, 5)? (a) (4, 8) (b) (2, 1) (c) (8, 4) (d) (16, 8)
19. 19.What is the distance between the points (9, 2) and (13, 5)? (a) 6 (b) 5 (c) 7 (d) 25
20. 20.What is the midpoint of the line joining (5, 1) and (11, 13)? (a) (8, 7) (b) (7, 8) (c) (16, 14) (d) (3, 6)
21. 21.What is the distance between the points (8, 14) and (24, 2)? (a) 21 (b) 28 (c) 400 (d) 20
22. 22.What is the distance between the points (5, 8) and (11, 16)? (a) 10 (b) 11 (c) 100 (d) 14
23. 23.In which quadrant does the point (2, −5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
24. 24.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
25. 25.In which quadrant does the point (−5, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
26. 26.In which quadrant does the point (6, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
28. 28.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
29. 29.What is the distance between the points (5, 4) and (17, 9)? (a) 13 (b) 14 (c) 17 (d) 169
30. 30.What is the midpoint of the line joining (8, 0) and (20, 4)? (a) (28, 4) (b) (2, 14) (c) (14, 2) (d) (6, 2)
31. 31.What is the distance between the points (3, 24) and (11, 9)? (a) 289 (b) 17 (c) 18 (d) 23
32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
34. 34.What is the distance between the points (9, 13) and (18, 1)? (a) 21 (b) 15 (c) 225 (d) 16
35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
36. 36.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
37. 37.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
38. 38.In which quadrant does the point (4, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
39. 39.What is the midpoint of the line joining (2, 14) and (14, 8)? (a) (11, 8) (b) (6, 3) (c) (8, 11) (d) (16, 22)
40. 40.What is the midpoint of the line joining (6, 14) and (16, 8)? (a) (5, 3) (b) (12, 11) (c) (22, 22) (d) (11, 11)

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