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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 380 · 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 (4, 9) and (8, 12)? (a) 5 (b) 25 (c) 6 (d) 7
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  3. 3.What is the distance between the points (0, 5) and (3, 9)? (a) 7 (b) 25 (c) 5 (d) 6
  4. 4.In which quadrant does the point (4, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  5. 5.What is the distance between the points (0, 9) and (12, 18)? (a) 225 (b) 16 (c) 21 (d) 15
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  7. 7.What is the midpoint of the line joining (7, 18) and (15, 10)? (a) (14, 11) (b) (4, 4) (c) (22, 28) (d) (11, 14)
  8. 8.What is the distance between the points (1, 8) and (25, 1)? (a) 31 (b) 26 (c) 25 (d) 625
  9. 9.What is the midpoint of the line joining (7, 1) and (11, 13)? (a) (7, 9) (b) (2, 6) (c) (18, 14) (d) (9, 7)
  10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  12. 12.In which quadrant does the point (−7, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.What is the distance between the points (0, 17) and (12, 8)? (a) 16 (b) 21 (c) 15 (d) 225
  14. 14.In which quadrant does the point (−3, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (6, 2) and (8, 6)? (a) (4, 7) (b) (1, 2) (c) (14, 8) (d) (7, 4)
  16. 16.What is the midpoint of the line joining (4, 9) and (8, 3)? (a) (2, 3) (b) (7, 6) (c) (12, 12) (d) (6, 6)
  17. 17.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  18. 18.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.What is the midpoint of the line joining (7, 12) and (17, 0)? (a) (12, 6) (b) (6, 12) (c) (5, 6) (d) (24, 12)
  20. 20.In which quadrant does the point (−6, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  21. 21.In which quadrant does the point (−9, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  22. 22.What is the distance between the points (9, 1) and (33, 8)? (a) 26 (b) 25 (c) 31 (d) 625
  23. 23.What is the distance between the points (8, 5) and (12, 8)? (a) 25 (b) 5 (c) 7 (d) 6
  24. 24.What is the midpoint of the line joining (2, 4) and (4, 14)? (a) (3, 9) (b) (9, 3) (c) (1, 5) (d) (6, 18)
  25. 25.What is the distance between the points (4, 5) and (7, 9)? (a) 6 (b) 5 (c) 7 (d) 25
  26. 26.What is the midpoint of the line joining (10, 11) and (22, 3)? (a) (7, 16) (b) (32, 14) (c) (6, 4) (d) (16, 7)
  27. 27.What is the distance between the points (0, 6) and (24, 13)? (a) 26 (b) 625 (c) 31 (d) 25
  28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  29. 29.What is the midpoint of the line joining (8, 6) and (14, 16)? (a) (22, 22) (b) (12, 11) (c) (3, 5) (d) (11, 11)
  30. 30.What is the midpoint of the line joining (5, 12) and (13, 6)? (a) (9, 9) (b) (10, 9) (c) (18, 18) (d) (4, 3)
  31. 31.What is the distance between the points (1, 12) and (6, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  32. 32.What is the midpoint of the line joining (2, 1) and (6, 11)? (a) (4, 6) (b) (6, 4) (c) (8, 12) (d) (2, 5)
  33. 33.What is the midpoint of the line joining (3, 9) and (7, 3)? (a) (2, 3) (b) (5, 6) (c) (6, 5) (d) (10, 12)
  34. 34.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  35. 35.What is the midpoint of the line joining (3, 20) and (9, 10)? (a) (6, 15) (b) (3, 5) (c) (15, 6) (d) (12, 30)
  36. 36.What is the distance between the points (0, 24) and (8, 9)? (a) 289 (b) 23 (c) 17 (d) 18
  37. 37.What is the distance between the points (9, 17) and (25, 5)? (a) 28 (b) 400 (c) 20 (d) 21
  38. 38.In which quadrant does the point (2, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.What is the midpoint of the line joining (9, 12) and (13, 2)? (a) (7, 11) (b) (11, 7) (c) (22, 14) (d) (2, 5)
  40. 40.What is the distance between the points (5, 6) and (9, 9)? (a) 5 (b) 25 (c) 6 (d) 7

Answer key

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

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