Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 332 · 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.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (8, 10) and (14, 12)? (a) (12, 11) (b) (22, 22) (c) (3, 1) (d) (11, 11)
3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
4. 4.What is the distance between the points (3, 7) and (10, 31)? (a) 625 (b) 31 (c) 26 (d) 25
5. 5.What is the midpoint of the line joining (2, 9) and (10, 17)? (a) (6, 13) (b) (4, 4) (c) (12, 26) (d) (13, 6)
6. 6.What is the midpoint of the line joining (10, 11) and (16, 7)? (a) (26, 18) (b) (9, 13) (c) (3, 2) (d) (13, 9)
7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
8. 8.What is the midpoint of the line joining (1, 12) and (13, 8)? (a) (7, 10) (b) (10, 7) (c) (6, 2) (d) (14, 20)
9. 9.In which quadrant does the point (−6, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
12. 12.What is the midpoint of the line joining (9, 7) and (17, 3)? (a) (4, 2) (b) (13, 5) (c) (26, 10) (d) (5, 13)
13. 13.What is the midpoint of the line joining (1, 11) and (11, 1)? (a) (5, 5) (b) (12, 12) (c) (6, 6) (d) (7, 6)
14. 14.What is the distance between the points (8, 8) and (11, 4)? (a) 6 (b) 5 (c) 25 (d) 7
15. 15.What is the distance between the points (6, 16) and (14, 1)? (a) 289 (b) 17 (c) 18 (d) 23
16. 16.What is the distance between the points (8, 16) and (32, 9)? (a) 31 (b) 26 (c) 25 (d) 625
17. 17.What is the midpoint of the line joining (3, 15) and (5, 5)? (a) (8, 20) (b) (1, 5) (c) (4, 10) (d) (10, 4)
18. 18.What is the distance between the points (2, 25) and (9, 1)? (a) 26 (b) 31 (c) 625 (d) 25
19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
20. 20.What is the midpoint of the line joining (7, 7) and (15, 1)? (a) (11, 4) (b) (4, 3) (c) (4, 11) (d) (22, 8)
21. 21.In which quadrant does the point (−9, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
22. 22.What is the midpoint of the line joining (7, 0) and (9, 12)? (a) (16, 12) (b) (6, 8) (c) (8, 6) (d) (1, 6)
23. 23.What is the distance between the points (2, 6) and (8, 14)? (a) 100 (b) 11 (c) 14 (d) 10
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
25. 25.What is the distance between the points (6, 9) and (14, 15)? (a) 10 (b) 100 (c) 14 (d) 11
26. 26.What is the distance between the points (7, 28) and (14, 4)? (a) 31 (b) 25 (c) 26 (d) 625
27. 27.What is the midpoint of the line joining (7, 12) and (11, 8)? (a) (9, 10) (b) (18, 20) (c) (2, 2) (d) (10, 9)
28. 28.What is the midpoint of the line joining (7, 8) and (11, 0)? (a) (2, 4) (b) (4, 9) (c) (9, 4) (d) (18, 8)
29. 29.What is the distance between the points (4, 7) and (20, 19)? (a) 20 (b) 400 (c) 28 (d) 21
30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
31. 31.In which quadrant does the point (−8, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
32. 32.What is the distance between the points (9, 0) and (24, 8)? (a) 289 (b) 18 (c) 17 (d) 23
33. 33.What is the midpoint of the line joining (8, 8) and (20, 6)? (a) (6, 1) (b) (28, 14) (c) (14, 7) (d) (7, 14)
34. 34.What is the midpoint of the line joining (9, 12) and (11, 8)? (a) (11, 10) (b) (10, 10) (c) (1, 2) (d) (20, 20)
35. 35.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
36. 36.What is the distance between the points (9, 4) and (33, 11)? (a) 31 (b) 25 (c) 26 (d) 625
37. 37.What is the distance between the points (5, 15) and (10, 3)? (a) 169 (b) 13 (c) 14 (d) 17
38. 38.What is the midpoint of the line joining (3, 6) and (5, 0)? (a) (8, 6) (b) (1, 3) (c) (4, 3) (d) (3, 4)
39. 39.What is the distance between the points (1, 2) and (17, 14)? (a) 400 (b) 21 (c) 20 (d) 28
40. 40.In which quadrant does the point (−2, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

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