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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 444 · 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.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.In which quadrant does the point (−2, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  3. 3.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  5. 5.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  6. 6.What is the midpoint of the line joining (4, 14) and (6, 6)? (a) (5, 10) (b) (1, 4) (c) (10, 5) (d) (10, 20)
  7. 7.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  9. 9.What is the distance between the points (0, 2) and (12, 7)? (a) 169 (b) 17 (c) 14 (d) 13
  10. 10.In which quadrant does the point (−2, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  11. 11.What is the distance between the points (5, 24) and (12, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  12. 12.What is the distance between the points (5, 1) and (20, 9)? (a) 18 (b) 289 (c) 17 (d) 23
  13. 13.What is the midpoint of the line joining (8, 11) and (18, 7)? (a) (9, 13) (b) (26, 18) (c) (13, 9) (d) (5, 2)
  14. 14.What is the distance between the points (6, 15) and (11, 3)? (a) 13 (b) 17 (c) 14 (d) 169
  15. 15.What is the distance between the points (3, 2) and (11, 8)? (a) 100 (b) 10 (c) 11 (d) 14
  16. 16.What is the distance between the points (1, 16) and (17, 4)? (a) 21 (b) 400 (c) 20 (d) 28
  17. 17.What is the distance between the points (1, 10) and (13, 5)? (a) 14 (b) 17 (c) 169 (d) 13
  18. 18.What is the distance between the points (1, 7) and (16, 15)? (a) 17 (b) 23 (c) 289 (d) 18
  19. 19.What is the distance between the points (7, 3) and (10, 7)? (a) 7 (b) 25 (c) 5 (d) 6
  20. 20.In which quadrant does the point (−1, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (5, 6) and (15, 10)? (a) (10, 8) (b) (20, 16) (c) (8, 10) (d) (5, 2)
  22. 22.What is the distance between the points (5, 23) and (13, 8)? (a) 17 (b) 18 (c) 23 (d) 289
  23. 23.What is the distance between the points (3, 7) and (15, 16)? (a) 21 (b) 225 (c) 16 (d) 15
  24. 24.What is the distance between the points (8, 9) and (32, 16)? (a) 26 (b) 31 (c) 625 (d) 25
  25. 25.What is the distance between the points (6, 10) and (18, 5)? (a) 17 (b) 14 (c) 13 (d) 169
  26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  27. 27.What is the midpoint of the line joining (6, 10) and (8, 8)? (a) (1, 1) (b) (14, 18) (c) (7, 9) (d) (9, 7)
  28. 28.What is the distance between the points (7, 9) and (12, 21)? (a) 17 (b) 14 (c) 13 (d) 169
  29. 29.What is the distance between the points (9, 8) and (17, 23)? (a) 289 (b) 18 (c) 23 (d) 17
  30. 30.What is the distance between the points (4, 9) and (12, 15)? (a) 14 (b) 100 (c) 10 (d) 11
  31. 31.What is the midpoint of the line joining (3, 12) and (11, 8)? (a) (10, 7) (b) (14, 20) (c) (7, 10) (d) (4, 2)
  32. 32.What is the distance between the points (6, 4) and (9, 8)? (a) 25 (b) 5 (c) 6 (d) 7
  33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  34. 34.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  35. 35.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (0, 5) and (12, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  37. 37.What is the distance between the points (3, 16) and (9, 8)? (a) 100 (b) 11 (c) 10 (d) 14
  38. 38.What is the midpoint of the line joining (1, 10) and (7, 14)? (a) (12, 4) (b) (4, 12) (c) (3, 2) (d) (8, 24)
  39. 39.What is the midpoint of the line joining (6, 1) and (16, 5)? (a) (3, 11) (b) (5, 2) (c) (22, 6) (d) (11, 3)
  40. 40.What is the distance between the points (1, 17) and (10, 5)? (a) 16 (b) 21 (c) 15 (d) 225

Answer key

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

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