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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 919 · 40 questions
TalentJR

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.

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

Answer key

  1. 5
  2. 10
  3. (9, 5)
  4. 25
  5. 25
  6. 10
  7. 13
  8. 5
  9. First quadrant
  10. 17
  11. 13
  12. 10
  13. First quadrant
  14. 17
  15. Fourth quadrant
  16. 13
  17. 5
  18. 25
  19. 13
  20. First quadrant
  21. 25
  22. (12, 5)
  23. (9, 10)
  24. 17
  25. Second quadrant
  26. First quadrant
  27. 5
  28. 15
  29. 5
  30. (11, 6)
  31. Second quadrant
  32. 5
  33. (7, 11)
  34. 15
  35. 20
  36. 5
  37. (5, 13)
  38. (12, 10)
  39. Third quadrant
  40. Third quadrant

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