Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 135 · 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 (−2, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
2. 2.What is the midpoint of the line joining (0, 1) and (2, 13)? (a) (1, 7) (b) (1, 6) (c) (2, 14) (d) (7, 1)
3. 3.What is the midpoint of the line joining (5, 20) and (17, 8)? (a) (22, 28) (b) (11, 14) (c) (6, 6) (d) (14, 11)
4. 4.What is the distance between the points (6, 7) and (15, 19)? (a) 16 (b) 15 (c) 225 (d) 21
5. 5.What is the distance between the points (0, 14) and (6, 6)? (a) 100 (b) 10 (c) 14 (d) 11
6. 6.What is the distance between the points (4, 1) and (16, 17)? (a) 21 (b) 400 (c) 28 (d) 20
7. 7.What is the midpoint of the line joining (3, 3) and (15, 13)? (a) (8, 9) (b) (6, 5) (c) (9, 8) (d) (18, 16)
8. 8.What is the midpoint of the line joining (7, 10) and (19, 14)? (a) (13, 12) (b) (12, 13) (c) (26, 24) (d) (6, 2)
9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
10. 10.In which quadrant does the point (5, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
11. 11.What is the midpoint of the line joining (5, 6) and (13, 2)? (a) (9, 4) (b) (18, 8) (c) (4, 2) (d) (4, 9)
12. 12.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
14. 14.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
15. 15.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (0, 11) and (2, 9)? (a) (2, 20) (b) (1, 10) (c) (1, 1) (d) (10, 1)
17. 17.What is the distance between the points (7, 7) and (31, 14)? (a) 25 (b) 31 (c) 26 (d) 625
18. 18.What is the midpoint of the line joining (10, 2) and (12, 4)? (a) (11, 3) (b) (22, 6) (c) (3, 11) (d) (1, 1)
19. 19.What is the midpoint of the line joining (3, 2) and (7, 8)? (a) (10, 10) (b) (6, 5) (c) (5, 5) (d) (2, 3)
20. 20.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
22. 22.What is the midpoint of the line joining (0, 4) and (2, 12)? (a) (1, 4) (b) (8, 1) (c) (1, 8) (d) (2, 16)
23. 23.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
24. 24.What is the distance between the points (1, 6) and (17, 18)? (a) 400 (b) 28 (c) 20 (d) 21
25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
26. 26.What is the midpoint of the line joining (0, 8) and (2, 16)? (a) (2, 24) (b) (1, 12) (c) (1, 4) (d) (12, 1)
27. 27.In which quadrant does the point (3, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
28. 28.What is the distance between the points (3, 13) and (9, 5)? (a) 100 (b) 14 (c) 11 (d) 10
29. 29.What is the distance between the points (2, 4) and (9, 28)? (a) 625 (b) 25 (c) 26 (d) 31
30. 30.In which quadrant does the point (−5, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
31. 31.What is the midpoint of the line joining (2, 9) and (8, 17)? (a) (5, 13) (b) (10, 26) (c) (13, 5) (d) (3, 4)
32. 32.What is the distance between the points (9, 9) and (21, 14)? (a) 14 (b) 13 (c) 17 (d) 169
33. 33.In which quadrant does the point (−7, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
34. 34.What is the midpoint of the line joining (0, 6) and (8, 16)? (a) (8, 22) (b) (4, 5) (c) (4, 11) (d) (11, 4)
35. 35.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
36. 36.What is the midpoint of the line joining (0, 9) and (4, 13)? (a) (4, 22) (b) (11, 2) (c) (2, 2) (d) (2, 11)
37. 37.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
38. 38.What is the distance between the points (1, 0) and (16, 8)? (a) 23 (b) 289 (c) 17 (d) 18
39. 39.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
40. 40.In which quadrant does the point (1, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant

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