Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 236 · 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.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
2. 2.What is the distance between the points (0, 13) and (12, 8)? (a) 17 (b) 13 (c) 14 (d) 169
3. 3.In which quadrant does the point (3, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
4. 4.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
5. 5.What is the midpoint of the line joining (10, 7) and (12, 15)? (a) (11, 11) (b) (12, 11) (c) (1, 4) (d) (22, 22)
6. 6.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
7. 7.In which quadrant does the point (−9, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
8. 8.What is the distance between the points (6, 8) and (9, 4)? (a) 6 (b) 25 (c) 7 (d) 5
9. 9.What is the distance between the points (0, 6) and (8, 21)? (a) 17 (b) 289 (c) 18 (d) 23
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
11. 11.In which quadrant does the point (−6, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.In which quadrant does the point (−4, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
13. 13.In which quadrant does the point (−1, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
14. 14.What is the midpoint of the line joining (10, 13) and (18, 3)? (a) (28, 16) (b) (4, 5) (c) (14, 8) (d) (8, 14)
15. 15.What is the midpoint of the line joining (0, 0) and (2, 4)? (a) (2, 1) (b) (1, 2) (c) (2, 2) (d) (2, 4)
16. 16.What is the midpoint of the line joining (7, 15) and (17, 5)? (a) (12, 10) (b) (24, 20) (c) (5, 5) (d) (10, 12)
17. 17.What is the midpoint of the line joining (4, 16) and (6, 10)? (a) (5, 13) (b) (1, 3) (c) (10, 26) (d) (13, 5)
18. 18.In which quadrant does the point (−7, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
19. 19.What is the distance between the points (0, 21) and (8, 6)? (a) 18 (b) 17 (c) 23 (d) 289
20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
21. 21.What is the midpoint of the line joining (9, 2) and (15, 6)? (a) (12, 4) (b) (24, 8) (c) (3, 2) (d) (4, 12)
22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
23. 23.What is the midpoint of the line joining (6, 7) and (16, 9)? (a) (8, 11) (b) (11, 8) (c) (5, 1) (d) (22, 16)
24. 24.What is the midpoint of the line joining (9, 7) and (11, 19)? (a) (13, 10) (b) (10, 13) (c) (1, 6) (d) (20, 26)
25. 25.What is the distance between the points (2, 9) and (10, 15)? (a) 11 (b) 10 (c) 14 (d) 100
26. 26.What is the distance between the points (0, 8) and (3, 4)? (a) 7 (b) 5 (c) 6 (d) 25
27. 27.In which quadrant does the point (4, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
28. 28.What is the distance between the points (2, 9) and (6, 6)? (a) 6 (b) 5 (c) 25 (d) 7
29. 29.What is the midpoint of the line joining (8, 10) and (10, 12)? (a) (18, 22) (b) (9, 11) (c) (11, 9) (d) (1, 1)
30. 30.In which quadrant does the point (2, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
31. 31.What is the midpoint of the line joining (3, 14) and (9, 10)? (a) (6, 12) (b) (12, 6) (c) (12, 24) (d) (3, 2)
32. 32.What is the midpoint of the line joining (1, 6) and (7, 2)? (a) (5, 4) (b) (4, 4) (c) (3, 2) (d) (8, 8)
33. 33.What is the distance between the points (8, 8) and (24, 20)? (a) 20 (b) 400 (c) 21 (d) 28
34. 34.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
35. 35.In which quadrant does the point (2, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.What is the distance between the points (0, 5) and (7, 29)? (a) 31 (b) 25 (c) 26 (d) 625
37. 37.What is the distance between the points (2, 20) and (7, 8)? (a) 17 (b) 14 (c) 13 (d) 169
38. 38.In which quadrant does the point (9, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
39. 39.What is the midpoint of the line joining (4, 10) and (14, 14)? (a) (18, 24) (b) (5, 2) (c) (9, 12) (d) (12, 9)
40. 40.What is the distance between the points (2, 5) and (18, 17)? (a) 400 (b) 21 (c) 28 (d) 20

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