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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 44 · 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 (9, 2) and (11, 6)? (a) (10, 4) (b) (20, 8) (c) (1, 2) (d) (4, 10)
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  4. 4.In which quadrant does the point (3, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  6. 6.What is the distance between the points (5, 8) and (9, 11)? (a) 5 (b) 25 (c) 6 (d) 7
  7. 7.What is the distance between the points (7, 6) and (10, 10)? (a) 5 (b) 25 (c) 6 (d) 7
  8. 8.In which quadrant does the point (−9, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  9. 9.What is the midpoint of the line joining (1, 3) and (3, 1)? (a) (2, 2) (b) (3, 2) (c) (1, 1) (d) (4, 4)
  10. 10.What is the midpoint of the line joining (1, 3) and (5, 13)? (a) (3, 8) (b) (8, 3) (c) (6, 16) (d) (2, 5)
  11. 11.What is the distance between the points (1, 13) and (16, 5)? (a) 23 (b) 289 (c) 17 (d) 18
  12. 12.What is the distance between the points (7, 9) and (14, 33)? (a) 26 (b) 25 (c) 31 (d) 625
  13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  14. 14.What is the midpoint of the line joining (7, 13) and (13, 9)? (a) (11, 10) (b) (10, 11) (c) (3, 2) (d) (20, 22)
  15. 15.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  16. 16.What is the midpoint of the line joining (10, 15) and (22, 5)? (a) (6, 5) (b) (10, 16) (c) (16, 10) (d) (32, 20)
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  18. 18.In which quadrant does the point (8, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  19. 19.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.In which quadrant does the point (7, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (4, 16) and (8, 6)? (a) (6, 11) (b) (2, 5) (c) (11, 6) (d) (12, 22)
  22. 22.In which quadrant does the point (−1, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  23. 23.What is the distance between the points (0, 23) and (8, 8)? (a) 289 (b) 18 (c) 17 (d) 23
  24. 24.What is the distance between the points (8, 9) and (12, 12)? (a) 25 (b) 6 (c) 7 (d) 5
  25. 25.What is the midpoint of the line joining (8, 7) and (16, 5)? (a) (6, 12) (b) (24, 12) (c) (4, 1) (d) (12, 6)
  26. 26.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  27. 27.What is the midpoint of the line joining (6, 13) and (18, 3)? (a) (6, 5) (b) (24, 16) (c) (8, 12) (d) (12, 8)
  28. 28.What is the midpoint of the line joining (2, 5) and (8, 7)? (a) (3, 1) (b) (5, 6) (c) (6, 5) (d) (10, 12)
  29. 29.What is the midpoint of the line joining (5, 10) and (17, 16)? (a) (11, 13) (b) (13, 11) (c) (6, 3) (d) (22, 26)
  30. 30.In which quadrant does the point (−5, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the distance between the points (6, 5) and (9, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  32. 32.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  33. 33.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the distance between the points (5, 4) and (17, 13)? (a) 16 (b) 21 (c) 15 (d) 225
  35. 35.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.What is the midpoint of the line joining (8, 10) and (18, 22)? (a) (26, 32) (b) (13, 16) (c) (5, 6) (d) (16, 13)
  37. 37.In which quadrant does the point (−4, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the distance between the points (5, 0) and (29, 7)? (a) 26 (b) 25 (c) 625 (d) 31
  39. 39.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  40. 40.In which quadrant does the point (8, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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