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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 237 · 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 (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  3. 3.In which quadrant does the point (−9, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  4. 4.In which quadrant does the point (4, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  5. 5.What is the distance between the points (9, 8) and (24, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  6. 6.In which quadrant does the point (−7, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  8. 8.What is the midpoint of the line joining (5, 6) and (9, 8)? (a) (14, 14) (b) (7, 7) (c) (8, 7) (d) (2, 1)
  9. 9.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  11. 11.What is the midpoint of the line joining (5, 8) and (15, 18)? (a) (20, 26) (b) (5, 5) (c) (13, 10) (d) (10, 13)
  12. 12.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  13. 13.What is the distance between the points (2, 2) and (14, 11)? (a) 16 (b) 225 (c) 21 (d) 15
  14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  15. 15.In which quadrant does the point (4, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  17. 17.What is the distance between the points (7, 20) and (15, 5)? (a) 23 (b) 18 (c) 289 (d) 17
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  19. 19.In which quadrant does the point (9, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  20. 20.What is the midpoint of the line joining (0, 10) and (10, 2)? (a) (5, 4) (b) (6, 5) (c) (5, 6) (d) (10, 12)
  21. 21.What is the distance between the points (1, 12) and (6, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  22. 22.In which quadrant does the point (9, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  25. 25.In which quadrant does the point (−9, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  26. 26.What is the distance between the points (7, 11) and (22, 3)? (a) 289 (b) 17 (c) 18 (d) 23
  27. 27.What is the distance between the points (4, 16) and (16, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  28. 28.What is the distance between the points (2, 9) and (8, 1)? (a) 100 (b) 14 (c) 10 (d) 11
  29. 29.What is the distance between the points (5, 9) and (17, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  30. 30.What is the midpoint of the line joining (10, 1) and (20, 13)? (a) (30, 14) (b) (7, 15) (c) (15, 7) (d) (5, 6)
  31. 31.In which quadrant does the point (−4, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  32. 32.In which quadrant does the point (−9, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  33. 33.What is the midpoint of the line joining (6, 14) and (12, 10)? (a) (12, 9) (b) (3, 2) (c) (9, 12) (d) (18, 24)
  34. 34.What is the midpoint of the line joining (8, 1) and (10, 11)? (a) (1, 5) (b) (9, 6) (c) (18, 12) (d) (6, 9)
  35. 35.What is the midpoint of the line joining (10, 2) and (18, 14)? (a) (28, 16) (b) (14, 8) (c) (4, 6) (d) (8, 14)
  36. 36.What is the distance between the points (1, 9) and (10, 21)? (a) 225 (b) 16 (c) 21 (d) 15
  37. 37.What is the midpoint of the line joining (1, 16) and (13, 10)? (a) (13, 7) (b) (6, 3) (c) (14, 26) (d) (7, 13)
  38. 38.What is the distance between the points (6, 5) and (15, 17)? (a) 21 (b) 16 (c) 225 (d) 15
  39. 39.What is the midpoint of the line joining (8, 2) and (18, 8)? (a) (5, 13) (b) (13, 5) (c) (5, 3) (d) (26, 10)
  40. 40.What is the midpoint of the line joining (0, 4) and (8, 12)? (a) (4, 4) (b) (8, 4) (c) (4, 8) (d) (8, 16)

Answer key

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

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