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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 62 · 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, 8) and (3, 12)? (a) (2, 10) (b) (10, 2) (c) (1, 2) (d) (4, 20)
  2. 2.What is the distance between the points (2, 1) and (14, 17)? (a) 400 (b) 28 (c) 21 (d) 20
  3. 3.In which quadrant does the point (−2, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  4. 4.What is the distance between the points (8, 16) and (23, 8)? (a) 289 (b) 23 (c) 17 (d) 18
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  6. 6.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  7. 7.What is the distance between the points (1, 1) and (10, 13)? (a) 16 (b) 225 (c) 15 (d) 21
  8. 8.What is the distance between the points (1, 7) and (9, 13)? (a) 100 (b) 14 (c) 11 (d) 10
  9. 9.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  10. 10.In which quadrant does the point (−7, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  11. 11.In which quadrant does the point (1, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  12. 12.What is the distance between the points (5, 8) and (11, 16)? (a) 11 (b) 10 (c) 100 (d) 14
  13. 13.What is the distance between the points (3, 4) and (18, 12)? (a) 23 (b) 18 (c) 17 (d) 289
  14. 14.What is the distance between the points (7, 3) and (19, 12)? (a) 225 (b) 21 (c) 16 (d) 15
  15. 15.What is the distance between the points (8, 2) and (20, 18)? (a) 20 (b) 400 (c) 21 (d) 28
  16. 16.What is the distance between the points (5, 13) and (11, 5)? (a) 14 (b) 100 (c) 10 (d) 11
  17. 17.What is the distance between the points (2, 9) and (14, 14)? (a) 17 (b) 14 (c) 169 (d) 13
  18. 18.What is the distance between the points (1, 0) and (4, 4)? (a) 5 (b) 6 (c) 7 (d) 25
  19. 19.In which quadrant does the point (−9, −8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.What is the midpoint of the line joining (10, 9) and (20, 15)? (a) (12, 15) (b) (15, 12) (c) (30, 24) (d) (5, 3)
  21. 21.In which quadrant does the point (9, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.What is the distance between the points (2, 14) and (11, 2)? (a) 15 (b) 225 (c) 21 (d) 16
  23. 23.What is the distance between the points (9, 4) and (17, 19)? (a) 17 (b) 18 (c) 23 (d) 289
  24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  25. 25.What is the midpoint of the line joining (6, 6) and (18, 10)? (a) (12, 8) (b) (24, 16) (c) (8, 12) (d) (6, 2)
  26. 26.In which quadrant does the point (−6, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.In which quadrant does the point (−8, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.What is the distance between the points (6, 3) and (11, 15)? (a) 13 (b) 17 (c) 14 (d) 169
  29. 29.What is the distance between the points (1, 3) and (16, 11)? (a) 289 (b) 23 (c) 18 (d) 17
  30. 30.What is the distance between the points (5, 21) and (17, 5)? (a) 400 (b) 21 (c) 20 (d) 28
  31. 31.What is the distance between the points (3, 13) and (9, 5)? (a) 10 (b) 100 (c) 14 (d) 11
  32. 32.What is the midpoint of the line joining (2, 12) and (12, 4)? (a) (5, 4) (b) (7, 8) (c) (14, 16) (d) (8, 7)
  33. 33.What is the distance between the points (5, 4) and (14, 16)? (a) 15 (b) 16 (c) 225 (d) 21
  34. 34.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  36. 36.What is the midpoint of the line joining (7, 8) and (9, 0)? (a) (4, 8) (b) (8, 4) (c) (16, 8) (d) (1, 4)
  37. 37.In which quadrant does the point (1, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  38. 38.In which quadrant does the point (−9, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  39. 39.What is the distance between the points (6, 4) and (10, 1)? (a) 7 (b) 6 (c) 25 (d) 5
  40. 40.What is the midpoint of the line joining (10, 3) and (12, 7)? (a) (1, 2) (b) (5, 11) (c) (22, 10) (d) (11, 5)

Answer key

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

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