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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 335 · 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 (10, 14) and (20, 4)? (a) (5, 5) (b) (30, 18) (c) (9, 15) (d) (15, 9)
  2. 2.In which quadrant does the point (2, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  3. 3.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  4. 4.What is the midpoint of the line joining (9, 4) and (21, 8)? (a) (30, 12) (b) (15, 6) (c) (6, 2) (d) (6, 15)
  5. 5.What is the distance between the points (5, 7) and (17, 16)? (a) 16 (b) 15 (c) 21 (d) 225
  6. 6.In which quadrant does the point (3, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.In which quadrant does the point (7, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the distance between the points (1, 17) and (9, 2)? (a) 23 (b) 289 (c) 18 (d) 17
  9. 9.What is the midpoint of the line joining (7, 10) and (9, 14)? (a) (1, 2) (b) (16, 24) (c) (8, 12) (d) (12, 8)
  10. 10.In which quadrant does the point (−3, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.What is the distance between the points (5, 21) and (10, 9)? (a) 13 (b) 14 (c) 17 (d) 169
  12. 12.What is the distance between the points (7, 8) and (22, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  13. 13.In which quadrant does the point (8, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  14. 14.In which quadrant does the point (7, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  15. 15.What is the midpoint of the line joining (1, 7) and (9, 9)? (a) (4, 1) (b) (5, 8) (c) (10, 16) (d) (8, 5)
  16. 16.What is the distance between the points (7, 0) and (11, 3)? (a) 5 (b) 6 (c) 25 (d) 7
  17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  18. 18.What is the distance between the points (2, 0) and (10, 6)? (a) 10 (b) 14 (c) 11 (d) 100
  19. 19.What is the midpoint of the line joining (2, 21) and (8, 9)? (a) (5, 15) (b) (15, 5) (c) (3, 6) (d) (10, 30)
  20. 20.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  21. 21.What is the distance between the points (8, 1) and (14, 9)? (a) 14 (b) 100 (c) 11 (d) 10
  22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  24. 24.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  25. 25.What is the distance between the points (4, 8) and (12, 14)? (a) 14 (b) 100 (c) 10 (d) 11
  26. 26.What is the midpoint of the line joining (4, 17) and (8, 7)? (a) (12, 24) (b) (2, 5) (c) (6, 12) (d) (12, 6)
  27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  28. 28.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  29. 29.What is the distance between the points (5, 15) and (21, 3)? (a) 28 (b) 400 (c) 21 (d) 20
  30. 30.What is the distance between the points (9, 8) and (13, 11)? (a) 6 (b) 25 (c) 5 (d) 7
  31. 31.What is the distance between the points (7, 21) and (16, 9)? (a) 15 (b) 225 (c) 16 (d) 21
  32. 32.What is the distance between the points (0, 4) and (8, 10)? (a) 100 (b) 10 (c) 11 (d) 14
  33. 33.In which quadrant does the point (5, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (3, 9) and (6, 5)? (a) 6 (b) 7 (c) 25 (d) 5
  35. 35.In which quadrant does the point (−1, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  36. 36.What is the midpoint of the line joining (4, 7) and (6, 17)? (a) (1, 5) (b) (5, 12) (c) (10, 24) (d) (12, 5)
  37. 37.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  38. 38.What is the distance between the points (5, 8) and (20, 16)? (a) 23 (b) 18 (c) 17 (d) 289
  39. 39.In which quadrant does the point (7, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  40. 40.What is the distance between the points (6, 18) and (14, 3)? (a) 23 (b) 18 (c) 17 (d) 289

Answer key

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

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