Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 992 · 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 (3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
2. 2.What is the midpoint of the line joining (4, 10) and (12, 12)? (a) (11, 8) (b) (8, 11) (c) (16, 22) (d) (4, 1)
3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
4. 4.What is the midpoint of the line joining (0, 9) and (10, 3)? (a) (5, 3) (b) (10, 12) (c) (5, 6) (d) (6, 5)
5. 5.What is the distance between the points (4, 9) and (28, 16)? (a) 25 (b) 625 (c) 26 (d) 31
6. 6.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
7. 7.What is the distance between the points (0, 0) and (7, 24)? (a) 25 (b) 31 (c) 625 (d) 26
8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
9. 9.What is the distance between the points (4, 7) and (28, 14)? (a) 625 (b) 31 (c) 26 (d) 25
10. 10.What is the midpoint of the line joining (4, 4) and (16, 12)? (a) (6, 4) (b) (20, 16) (c) (10, 8) (d) (8, 10)
11. 11.What is the midpoint of the line joining (2, 1) and (6, 5)? (a) (2, 2) (b) (3, 4) (c) (8, 6) (d) (4, 3)
12. 12.What is the midpoint of the line joining (6, 8) and (10, 14)? (a) (2, 3) (b) (11, 8) (c) (16, 22) (d) (8, 11)
13. 13.What is the midpoint of the line joining (6, 15) and (8, 9)? (a) (7, 12) (b) (1, 3) (c) (12, 7) (d) (14, 24)
14. 14.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
15. 15.What is the distance between the points (4, 1) and (8, 4)? (a) 6 (b) 25 (c) 5 (d) 7
16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
17. 17.What is the midpoint of the line joining (0, 2) and (6, 12)? (a) (6, 14) (b) (3, 7) (c) (7, 3) (d) (3, 5)
18. 18.What is the midpoint of the line joining (5, 6) and (7, 16)? (a) (1, 5) (b) (12, 22) (c) (11, 6) (d) (6, 11)
19. 19.In which quadrant does the point (8, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
20. 20.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
22. 22.What is the distance between the points (1, 12) and (6, 0)? (a) 14 (b) 169 (c) 17 (d) 13
23. 23.What is the distance between the points (2, 2) and (7, 14)? (a) 169 (b) 13 (c) 14 (d) 17
24. 24.What is the midpoint of the line joining (1, 20) and (13, 8)? (a) (14, 28) (b) (14, 7) (c) (6, 6) (d) (7, 14)
25. 25.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
26. 26.What is the distance between the points (4, 0) and (12, 6)? (a) 10 (b) 11 (c) 14 (d) 100
27. 27.What is the distance between the points (7, 6) and (10, 10)? (a) 7 (b) 25 (c) 6 (d) 5
28. 28.What is the midpoint of the line joining (2, 1) and (4, 5)? (a) (6, 6) (b) (3, 3) (c) (1, 2) (d) (4, 3)
29. 29.In which quadrant does the point (4, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
30. 30.What is the midpoint of the line joining (8, 2) and (12, 8)? (a) (5, 10) (b) (2, 3) (c) (10, 5) (d) (20, 10)
31. 31.In which quadrant does the point (−7, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
32. 32.In which quadrant does the point (−5, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
33. 33.What is the midpoint of the line joining (2, 9) and (6, 3)? (a) (4, 6) (b) (8, 12) (c) (6, 4) (d) (2, 3)
34. 34.What is the midpoint of the line joining (1, 11) and (13, 9)? (a) (6, 1) (b) (7, 10) (c) (10, 7) (d) (14, 20)
35. 35.What is the midpoint of the line joining (1, 9) and (11, 17)? (a) (12, 26) (b) (6, 13) (c) (5, 4) (d) (13, 6)
36. 36.In which quadrant does the point (6, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
37. 37.In which quadrant does the point (−1, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
38. 38.What is the distance between the points (6, 7) and (9, 11)? (a) 25 (b) 7 (c) 6 (d) 5
39. 39.What is the midpoint of the line joining (2, 16) and (10, 4)? (a) (6, 10) (b) (4, 6) (c) (12, 20) (d) (10, 6)
40. 40.What is the midpoint of the line joining (3, 11) and (5, 3)? (a) (8, 14) (b) (4, 7) (c) (1, 4) (d) (7, 4)

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