Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 976 · 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, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
2. 2.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
3. 3.What is the midpoint of the line joining (9, 1) and (19, 5)? (a) (5, 2) (b) (28, 6) (c) (14, 3) (d) (3, 14)
4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
5. 5.In which quadrant does the point (−5, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
6. 6.What is the midpoint of the line joining (2, 1) and (4, 9)? (a) (6, 10) (b) (3, 5) (c) (5, 3) (d) (1, 4)
7. 7.In which quadrant does the point (−4, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
8. 8.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
9. 9.What is the distance between the points (5, 14) and (17, 5)? (a) 225 (b) 16 (c) 15 (d) 21
10. 10.What is the distance between the points (0, 15) and (6, 7)? (a) 14 (b) 10 (c) 100 (d) 11
11. 11.What is the distance between the points (1, 3) and (13, 8)? (a) 17 (b) 13 (c) 169 (d) 14
12. 12.What is the distance between the points (8, 6) and (14, 14)? (a) 100 (b) 11 (c) 10 (d) 14
13. 13.What is the midpoint of the line joining (2, 6) and (8, 0)? (a) (3, 5) (b) (10, 6) (c) (5, 3) (d) (3, 3)
14. 14.In which quadrant does the point (3, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
15. 15.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (0, 1) and (10, 7)? (a) (5, 4) (b) (5, 3) (c) (4, 5) (d) (10, 8)
17. 17.In which quadrant does the point (6, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
18. 18.What is the distance between the points (6, 18) and (15, 6)? (a) 16 (b) 21 (c) 225 (d) 15
19. 19.What is the midpoint of the line joining (2, 1) and (10, 7)? (a) (12, 8) (b) (6, 4) (c) (4, 6) (d) (4, 3)
20. 20.What is the distance between the points (3, 15) and (9, 7)? (a) 11 (b) 100 (c) 10 (d) 14
21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
22. 22.What is the distance between the points (0, 9) and (15, 17)? (a) 23 (b) 289 (c) 18 (d) 17
23. 23.What is the midpoint of the line joining (6, 2) and (8, 10)? (a) (1, 4) (b) (14, 12) (c) (6, 7) (d) (7, 6)
24. 24.What is the distance between the points (6, 8) and (30, 1)? (a) 31 (b) 25 (c) 625 (d) 26
25. 25.What is the midpoint of the line joining (6, 0) and (8, 4)? (a) (7, 2) (b) (2, 7) (c) (14, 4) (d) (1, 2)
26. 26.What is the distance between the points (0, 4) and (3, 0)? (a) 6 (b) 7 (c) 5 (d) 25
27. 27.What is the midpoint of the line joining (7, 4) and (17, 0)? (a) (24, 4) (b) (12, 2) (c) (5, 2) (d) (2, 12)
28. 28.In which quadrant does the point (7, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
29. 29.What is the midpoint of the line joining (2, 10) and (6, 14)? (a) (4, 12) (b) (2, 2) (c) (8, 24) (d) (12, 4)
30. 30.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
31. 31.What is the distance between the points (3, 19) and (19, 7)? (a) 21 (b) 400 (c) 28 (d) 20
32. 32.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
33. 33.In which quadrant does the point (5, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
34. 34.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
35. 35.What is the midpoint of the line joining (3, 10) and (11, 0)? (a) (4, 5) (b) (14, 10) (c) (5, 7) (d) (7, 5)
36. 36.In which quadrant does the point (−4, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
37. 37.What is the midpoint of the line joining (0, 9) and (4, 19)? (a) (4, 28) (b) (2, 14) (c) (14, 2) (d) (2, 5)
38. 38.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
39. 39.In which quadrant does the point (−2, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
40. 40.What is the midpoint of the line joining (6, 6) and (12, 12)? (a) (9, 9) (b) (18, 18) (c) (10, 9) (d) (3, 3)

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