Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 931 · 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 (−8, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
2. 2.What is the distance between the points (2, 9) and (14, 14)? (a) 14 (b) 17 (c) 13 (d) 169
3. 3.In which quadrant does the point (−8, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
4. 4.What is the midpoint of the line joining (4, 16) and (6, 6)? (a) (1, 5) (b) (5, 11) (c) (10, 22) (d) (11, 5)
5. 5.What is the midpoint of the line joining (5, 9) and (17, 5)? (a) (11, 7) (b) (6, 2) (c) (22, 14) (d) (7, 11)
6. 6.What is the midpoint of the line joining (3, 9) and (7, 7)? (a) (5, 8) (b) (8, 5) (c) (10, 16) (d) (2, 1)
7. 7.What is the distance between the points (4, 12) and (8, 9)? (a) 25 (b) 5 (c) 7 (d) 6
8. 8.What is the distance between the points (8, 3) and (13, 15)? (a) 169 (b) 13 (c) 14 (d) 17
9. 9.In which quadrant does the point (−1, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
10. 10.In which quadrant does the point (−2, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
11. 11.What is the midpoint of the line joining (8, 8) and (18, 12)? (a) (26, 20) (b) (13, 10) (c) (10, 13) (d) (5, 2)
12. 12.What is the distance between the points (0, 24) and (8, 9)? (a) 17 (b) 18 (c) 23 (d) 289
13. 13.What is the distance between the points (9, 15) and (14, 3)? (a) 17 (b) 13 (c) 14 (d) 169
14. 14.What is the distance between the points (5, 0) and (11, 8)? (a) 11 (b) 14 (c) 100 (d) 10
15. 15.What is the distance between the points (9, 9) and (17, 15)? (a) 10 (b) 14 (c) 100 (d) 11
16. 16.What is the distance between the points (2, 0) and (8, 8)? (a) 100 (b) 14 (c) 10 (d) 11
17. 17.What is the midpoint of the line joining (10, 6) and (22, 8)? (a) (32, 14) (b) (7, 16) (c) (6, 1) (d) (16, 7)
18. 18.What is the midpoint of the line joining (7, 15) and (17, 5)? (a) (24, 20) (b) (5, 5) (c) (10, 12) (d) (12, 10)
19. 19.What is the distance between the points (7, 8) and (19, 13)? (a) 17 (b) 169 (c) 14 (d) 13
20. 20.In which quadrant does the point (2, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
21. 21.What is the distance between the points (1, 7) and (8, 31)? (a) 25 (b) 625 (c) 26 (d) 31
22. 22.What is the distance between the points (3, 11) and (15, 2)? (a) 15 (b) 21 (c) 225 (d) 16
23. 23.What is the distance between the points (0, 4) and (12, 9)? (a) 169 (b) 13 (c) 17 (d) 14
24. 24.What is the distance between the points (0, 6) and (6, 14)? (a) 10 (b) 100 (c) 11 (d) 14
25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
27. 27.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
28. 28.What is the distance between the points (5, 28) and (12, 4)? (a) 25 (b) 31 (c) 625 (d) 26
29. 29.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
30. 30.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
31. 31.What is the midpoint of the line joining (4, 1) and (12, 3)? (a) (8, 2) (b) (4, 1) (c) (2, 8) (d) (16, 4)
32. 32.What is the distance between the points (7, 6) and (15, 12)? (a) 100 (b) 11 (c) 14 (d) 10
33. 33.What is the distance between the points (4, 7) and (28, 0)? (a) 625 (b) 25 (c) 31 (d) 26
34. 34.What is the distance between the points (3, 5) and (19, 17)? (a) 400 (b) 20 (c) 28 (d) 21
35. 35.What is the distance between the points (6, 8) and (11, 20)? (a) 14 (b) 13 (c) 17 (d) 169
36. 36.In which quadrant does the point (9, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.What is the midpoint of the line joining (10, 6) and (16, 2)? (a) (3, 2) (b) (4, 13) (c) (13, 4) (d) (26, 8)
38. 38.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
39. 39.What is the midpoint of the line joining (0, 10) and (4, 6)? (a) (8, 2) (b) (2, 8) (c) (2, 2) (d) (4, 16)
40. 40.What is the midpoint of the line joining (8, 9) and (14, 7)? (a) (8, 11) (b) (22, 16) (c) (11, 8) (d) (3, 1)

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