Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 912 · 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, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
2. 2.What is the distance between the points (7, 5) and (12, 17)? (a) 14 (b) 17 (c) 169 (d) 13
3. 3.What is the distance between the points (5, 3) and (14, 15)? (a) 225 (b) 16 (c) 21 (d) 15
4. 4.In which quadrant does the point (−3, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
5. 5.What is the midpoint of the line joining (1, 4) and (3, 12)? (a) (4, 16) (b) (2, 8) (c) (8, 2) (d) (1, 4)
6. 6.What is the distance between the points (2, 6) and (14, 1)? (a) 169 (b) 14 (c) 17 (d) 13
7. 7.In which quadrant does the point (8, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
8. 8.What is the midpoint of the line joining (1, 12) and (5, 0)? (a) (2, 6) (b) (6, 12) (c) (6, 3) (d) (3, 6)
9. 9.What is the distance between the points (4, 17) and (9, 5)? (a) 14 (b) 169 (c) 17 (d) 13
10. 10.What is the midpoint of the line joining (9, 8) and (17, 10)? (a) (4, 1) (b) (9, 13) (c) (26, 18) (d) (13, 9)
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
12. 12.In which quadrant does the point (−2, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
13. 13.What is the midpoint of the line joining (5, 6) and (15, 18)? (a) (5, 6) (b) (12, 10) (c) (20, 24) (d) (10, 12)
14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
15. 15.In which quadrant does the point (−5, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
16. 16.What is the distance between the points (9, 3) and (15, 11)? (a) 11 (b) 100 (c) 10 (d) 14
17. 17.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
18. 18.What is the distance between the points (4, 5) and (8, 2)? (a) 5 (b) 6 (c) 7 (d) 25
19. 19.What is the distance between the points (0, 7) and (4, 10)? (a) 7 (b) 25 (c) 6 (d) 5
20. 20.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
22. 22.What is the distance between the points (0, 19) and (5, 7)? (a) 14 (b) 17 (c) 13 (d) 169
23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
24. 24.What is the midpoint of the line joining (0, 14) and (4, 10)? (a) (2, 2) (b) (12, 2) (c) (4, 24) (d) (2, 12)
25. 25.What is the midpoint of the line joining (9, 6) and (21, 16)? (a) (6, 5) (b) (11, 15) (c) (15, 11) (d) (30, 22)
26. 26.What is the distance between the points (3, 3) and (7, 6)? (a) 25 (b) 5 (c) 7 (d) 6
27. 27.In which quadrant does the point (2, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
28. 28.What is the midpoint of the line joining (4, 1) and (8, 13)? (a) (2, 6) (b) (7, 6) (c) (6, 7) (d) (12, 14)
29. 29.What is the distance between the points (3, 8) and (27, 1)? (a) 26 (b) 31 (c) 625 (d) 25
30. 30.What is the distance between the points (7, 10) and (10, 6)? (a) 25 (b) 7 (c) 5 (d) 6
31. 31.What is the distance between the points (4, 6) and (19, 14)? (a) 18 (b) 289 (c) 17 (d) 23
32. 32.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
33. 33.In which quadrant does the point (7, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
34. 34.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
35. 35.What is the midpoint of the line joining (2, 0) and (10, 6)? (a) (6, 3) (b) (4, 3) (c) (3, 6) (d) (12, 6)
36. 36.What is the distance between the points (1, 0) and (5, 3)? (a) 25 (b) 5 (c) 7 (d) 6
37. 37.What is the distance between the points (3, 8) and (12, 20)? (a) 21 (b) 225 (c) 15 (d) 16
38. 38.What is the midpoint of the line joining (5, 4) and (15, 14)? (a) (5, 5) (b) (9, 10) (c) (10, 9) (d) (20, 18)
39. 39.What is the distance between the points (6, 1) and (30, 8)? (a) 625 (b) 26 (c) 31 (d) 25
40. 40.What is the midpoint of the line joining (4, 16) and (16, 6)? (a) (10, 11) (b) (6, 5) (c) (11, 10) (d) (20, 22)

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