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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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