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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 60 · 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 midpoint of the line joining (1, 9) and (11, 21)? (a) (15, 6) (b) (12, 30) (c) (5, 6) (d) (6, 15)
  2. 2.What is the distance between the points (5, 27) and (12, 3)? (a) 25 (b) 26 (c) 31 (d) 625
  3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  5. 5.What is the midpoint of the line joining (8, 13) and (10, 1)? (a) (7, 9) (b) (18, 14) (c) (1, 6) (d) (9, 7)
  6. 6.In which quadrant does the point (5, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  7. 7.What is the midpoint of the line joining (9, 8) and (11, 16)? (a) (10, 12) (b) (20, 24) (c) (12, 10) (d) (1, 4)
  8. 8.What is the distance between the points (1, 14) and (25, 7)? (a) 31 (b) 25 (c) 26 (d) 625
  9. 9.What is the distance between the points (5, 2) and (13, 17)? (a) 23 (b) 17 (c) 18 (d) 289
  10. 10.What is the distance between the points (7, 2) and (22, 10)? (a) 17 (b) 289 (c) 23 (d) 18
  11. 11.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  12. 12.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  13. 13.What is the distance between the points (1, 0) and (17, 12)? (a) 20 (b) 21 (c) 28 (d) 400
  14. 14.What is the midpoint of the line joining (3, 12) and (15, 0)? (a) (18, 12) (b) (6, 9) (c) (6, 6) (d) (9, 6)
  15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  16. 16.What is the distance between the points (8, 1) and (32, 8)? (a) 625 (b) 26 (c) 31 (d) 25
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  18. 18.In which quadrant does the point (−2, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  19. 19.In which quadrant does the point (4, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the distance between the points (2, 9) and (10, 15)? (a) 100 (b) 10 (c) 11 (d) 14
  21. 21.What is the distance between the points (5, 5) and (12, 29)? (a) 25 (b) 625 (c) 26 (d) 31
  22. 22.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  23. 23.What is the midpoint of the line joining (1, 4) and (13, 8)? (a) (7, 6) (b) (6, 7) (c) (14, 12) (d) (6, 2)
  24. 24.What is the distance between the points (6, 9) and (12, 1)? (a) 14 (b) 100 (c) 10 (d) 11
  25. 25.What is the distance between the points (7, 3) and (16, 15)? (a) 21 (b) 15 (c) 225 (d) 16
  26. 26.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  27. 27.What is the midpoint of the line joining (6, 6) and (10, 8)? (a) (8, 7) (b) (16, 14) (c) (2, 1) (d) (7, 8)
  28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  30. 30.In which quadrant does the point (−6, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (8, 10) and (10, 6)? (a) (8, 9) (b) (18, 16) (c) (1, 2) (d) (9, 8)
  32. 32.What is the midpoint of the line joining (3, 12) and (7, 10)? (a) (2, 1) (b) (11, 5) (c) (10, 22) (d) (5, 11)
  33. 33.In which quadrant does the point (4, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  34. 34.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the midpoint of the line joining (4, 0) and (10, 12)? (a) (7, 6) (b) (6, 7) (c) (14, 12) (d) (3, 6)
  37. 37.What is the distance between the points (9, 5) and (17, 11)? (a) 10 (b) 11 (c) 14 (d) 100
  38. 38.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  39. 39.What is the midpoint of the line joining (2, 8) and (6, 18)? (a) (8, 26) (b) (2, 5) (c) (4, 13) (d) (13, 4)
  40. 40.What is the distance between the points (8, 15) and (14, 7)? (a) 11 (b) 10 (c) 100 (d) 14

Answer key

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

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