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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 559 · 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.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  3. 3.What is the midpoint of the line joining (4, 5) and (8, 15)? (a) (12, 20) (b) (10, 6) (c) (2, 5) (d) (6, 10)
  4. 4.What is the distance between the points (1, 5) and (17, 17)? (a) 21 (b) 28 (c) 400 (d) 20
  5. 5.What is the midpoint of the line joining (7, 16) and (9, 10)? (a) (8, 13) (b) (1, 3) (c) (13, 8) (d) (16, 26)
  6. 6.What is the midpoint of the line joining (9, 5) and (21, 1)? (a) (6, 2) (b) (30, 6) (c) (15, 3) (d) (3, 15)
  7. 7.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  8. 8.In which quadrant does the point (6, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  10. 10.In which quadrant does the point (3, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  12. 12.What is the distance between the points (9, 22) and (17, 7)? (a) 289 (b) 23 (c) 17 (d) 18
  13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  14. 14.What is the distance between the points (2, 13) and (8, 5)? (a) 14 (b) 100 (c) 11 (d) 10
  15. 15.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  16. 16.What is the distance between the points (2, 17) and (8, 9)? (a) 14 (b) 10 (c) 100 (d) 11
  17. 17.What is the distance between the points (1, 15) and (9, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  18. 18.In which quadrant does the point (−6, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  19. 19.What is the distance between the points (8, 2) and (14, 10)? (a) 100 (b) 11 (c) 14 (d) 10
  20. 20.What is the midpoint of the line joining (7, 2) and (9, 10)? (a) (1, 4) (b) (8, 6) (c) (16, 12) (d) (6, 8)
  21. 21.What is the midpoint of the line joining (1, 10) and (3, 20)? (a) (4, 30) (b) (1, 5) (c) (2, 15) (d) (15, 2)
  22. 22.What is the distance between the points (7, 7) and (13, 15)? (a) 11 (b) 10 (c) 14 (d) 100
  23. 23.What is the midpoint of the line joining (3, 3) and (11, 13)? (a) (4, 5) (b) (8, 7) (c) (7, 8) (d) (14, 16)
  24. 24.In which quadrant does the point (−9, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  25. 25.What is the midpoint of the line joining (6, 2) and (8, 4)? (a) (3, 7) (b) (7, 3) (c) (1, 1) (d) (14, 6)
  26. 26.In which quadrant does the point (−8, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  27. 27.What is the distance between the points (9, 12) and (33, 5)? (a) 625 (b) 31 (c) 25 (d) 26
  28. 28.What is the distance between the points (2, 4) and (8, 12)? (a) 14 (b) 100 (c) 11 (d) 10
  29. 29.What is the midpoint of the line joining (2, 4) and (4, 14)? (a) (3, 9) (b) (9, 3) (c) (6, 18) (d) (1, 5)
  30. 30.What is the distance between the points (7, 19) and (15, 4)? (a) 18 (b) 289 (c) 17 (d) 23
  31. 31.What is the midpoint of the line joining (2, 9) and (10, 7)? (a) (8, 6) (b) (4, 1) (c) (6, 8) (d) (12, 16)
  32. 32.What is the distance between the points (7, 32) and (14, 8)? (a) 25 (b) 31 (c) 26 (d) 625
  33. 33.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  34. 34.What is the distance between the points (6, 24) and (18, 8)? (a) 28 (b) 21 (c) 400 (d) 20
  35. 35.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  36. 36.What is the distance between the points (7, 9) and (12, 21)? (a) 17 (b) 169 (c) 14 (d) 13
  37. 37.What is the midpoint of the line joining (7, 14) and (19, 6)? (a) (10, 13) (b) (6, 4) (c) (26, 20) (d) (13, 10)
  38. 38.What is the midpoint of the line joining (10, 4) and (22, 0)? (a) (16, 2) (b) (6, 2) (c) (32, 4) (d) (2, 16)
  39. 39.What is the midpoint of the line joining (0, 15) and (6, 9)? (a) (12, 3) (b) (3, 3) (c) (3, 12) (d) (6, 24)
  40. 40.In which quadrant does the point (−8, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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