Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 881 · 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.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
2. 2.What is the midpoint of the line joining (5, 1) and (11, 3)? (a) (8, 2) (b) (16, 4) (c) (3, 1) (d) (2, 8)
3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
4. 4.What is the distance between the points (5, 9) and (17, 4)? (a) 169 (b) 17 (c) 14 (d) 13
5. 5.In which quadrant does the point (−4, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
6. 6.What is the distance between the points (7, 3) and (31, 10)? (a) 25 (b) 31 (c) 26 (d) 625
7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
9. 9.What is the midpoint of the line joining (5, 0) and (11, 10)? (a) (3, 5) (b) (8, 5) (c) (16, 10) (d) (5, 8)
10. 10.What is the midpoint of the line joining (10, 3) and (20, 5)? (a) (15, 4) (b) (4, 15) (c) (5, 1) (d) (30, 8)
11. 11.What is the midpoint of the line joining (3, 7) and (7, 5)? (a) (6, 5) (b) (10, 12) (c) (2, 1) (d) (5, 6)
12. 12.What is the distance between the points (2, 6) and (8, 14)? (a) 10 (b) 100 (c) 11 (d) 14
13. 13.In which quadrant does the point (−8, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
14. 14.What is the distance between the points (7, 3) and (19, 12)? (a) 21 (b) 16 (c) 225 (d) 15
15. 15.In which quadrant does the point (9, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (8, 16) and (12, 6)? (a) (2, 5) (b) (20, 22) (c) (11, 10) (d) (10, 11)
17. 17.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
18. 18.What is the distance between the points (7, 11) and (19, 6)? (a) 17 (b) 14 (c) 169 (d) 13
19. 19.What is the midpoint of the line joining (2, 20) and (8, 8)? (a) (10, 28) (b) (3, 6) (c) (5, 14) (d) (14, 5)
20. 20.What is the distance between the points (0, 2) and (9, 14)? (a) 225 (b) 16 (c) 21 (d) 15
21. 21.In which quadrant does the point (−4, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
22. 22.What is the distance between the points (1, 13) and (13, 8)? (a) 169 (b) 17 (c) 14 (d) 13
23. 23.What is the midpoint of the line joining (2, 15) and (6, 9)? (a) (4, 12) (b) (8, 24) (c) (2, 3) (d) (12, 4)
24. 24.What is the distance between the points (0, 20) and (16, 8)? (a) 21 (b) 400 (c) 20 (d) 28
25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
26. 26.What is the midpoint of the line joining (1, 10) and (3, 20)? (a) (1, 5) (b) (4, 30) (c) (2, 15) (d) (15, 2)
27. 27.In which quadrant does the point (8, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
28. 28.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
29. 29.What is the distance between the points (5, 20) and (21, 8)? (a) 20 (b) 28 (c) 400 (d) 21
30. 30.In which quadrant does the point (−5, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
31. 31.What is the distance between the points (1, 21) and (10, 9)? (a) 15 (b) 225 (c) 16 (d) 21
32. 32.In which quadrant does the point (−7, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
33. 33.What is the distance between the points (8, 5) and (24, 17)? (a) 20 (b) 400 (c) 28 (d) 21
34. 34.What is the distance between the points (0, 14) and (6, 6)? (a) 11 (b) 14 (c) 100 (d) 10
35. 35.What is the distance between the points (6, 32) and (13, 8)? (a) 25 (b) 625 (c) 31 (d) 26
36. 36.What is the midpoint of the line joining (7, 10) and (17, 14)? (a) (12, 12) (b) (13, 12) (c) (24, 24) (d) (5, 2)
37. 37.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
38. 38.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
39. 39.What is the midpoint of the line joining (1, 8) and (7, 18)? (a) (3, 5) (b) (13, 4) (c) (4, 13) (d) (8, 26)
40. 40.What is the midpoint of the line joining (8, 10) and (14, 6)? (a) (22, 16) (b) (3, 2) (c) (11, 8) (d) (8, 11)

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