Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 402 · 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 (−4, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (9, 9) and (13, 13)? (a) (22, 22) (b) (12, 11) (c) (11, 11) (d) (2, 2)
3. 3.In which quadrant does the point (2, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
4. 4.What is the midpoint of the line joining (4, 1) and (8, 3)? (a) (2, 6) (b) (12, 4) (c) (2, 1) (d) (6, 2)
5. 5.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
6. 6.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
7. 7.What is the distance between the points (2, 21) and (18, 9)? (a) 400 (b) 28 (c) 21 (d) 20
8. 8.What is the distance between the points (7, 2) and (16, 14)? (a) 225 (b) 16 (c) 15 (d) 21
9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
10. 10.In which quadrant does the point (8, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
12. 12.What is the midpoint of the line joining (1, 20) and (11, 8)? (a) (14, 6) (b) (12, 28) (c) (5, 6) (d) (6, 14)
13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
14. 14.What is the midpoint of the line joining (8, 8) and (18, 16)? (a) (12, 13) (b) (13, 12) (c) (26, 24) (d) (5, 4)
15. 15.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
16. 16.What is the distance between the points (8, 11) and (16, 5)? (a) 11 (b) 100 (c) 14 (d) 10
17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
18. 18.In which quadrant does the point (7, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
19. 19.What is the distance between the points (4, 14) and (13, 2)? (a) 21 (b) 15 (c) 225 (d) 16
20. 20.In which quadrant does the point (5, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
21. 21.What is the distance between the points (6, 5) and (30, 12)? (a) 31 (b) 26 (c) 625 (d) 25
22. 22.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
23. 23.What is the distance between the points (8, 1) and (14, 9)? (a) 10 (b) 100 (c) 14 (d) 11
24. 24.What is the distance between the points (7, 14) and (19, 9)? (a) 13 (b) 17 (c) 14 (d) 169
25. 25.In which quadrant does the point (−1, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
26. 26.What is the midpoint of the line joining (1, 9) and (11, 1)? (a) (12, 10) (b) (5, 6) (c) (6, 5) (d) (5, 4)
27. 27.What is the distance between the points (4, 7) and (11, 31)? (a) 26 (b) 31 (c) 25 (d) 625
28. 28.In which quadrant does the point (5, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
29. 29.What is the midpoint of the line joining (9, 13) and (21, 9)? (a) (11, 15) (b) (30, 22) (c) (15, 11) (d) (6, 2)
30. 30.What is the midpoint of the line joining (8, 15) and (20, 7)? (a) (14, 11) (b) (6, 4) (c) (28, 22) (d) (11, 14)
31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
32. 32.What is the midpoint of the line joining (5, 1) and (7, 5)? (a) (3, 6) (b) (1, 2) (c) (6, 3) (d) (12, 6)
33. 33.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
34. 34.In which quadrant does the point (−9, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
35. 35.What is the distance between the points (8, 2) and (23, 10)? (a) 289 (b) 17 (c) 18 (d) 23
36. 36.What is the midpoint of the line joining (9, 17) and (13, 9)? (a) (2, 4) (b) (22, 26) (c) (13, 11) (d) (11, 13)
37. 37.What is the midpoint of the line joining (4, 8) and (10, 12)? (a) (3, 2) (b) (7, 10) (c) (10, 7) (d) (14, 20)
38. 38.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
39. 39.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
40. 40.In which quadrant does the point (−6, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

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