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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 572 · 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 (6, 6) and (12, 0)? (a) (3, 3) (b) (3, 9) (c) (18, 6) (d) (9, 3)
  2. 2.What is the distance between the points (1, 9) and (9, 24)? (a) 18 (b) 289 (c) 17 (d) 23
  3. 3.What is the midpoint of the line joining (4, 9) and (8, 11)? (a) (2, 1) (b) (10, 6) (c) (12, 20) (d) (6, 10)
  4. 4.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  6. 6.What is the midpoint of the line joining (6, 9) and (14, 15)? (a) (4, 3) (b) (12, 10) (c) (20, 24) (d) (10, 12)
  7. 7.In which quadrant does the point (6, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  9. 9.What is the distance between the points (9, 9) and (13, 12)? (a) 5 (b) 6 (c) 25 (d) 7
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  13. 13.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.What is the distance between the points (6, 8) and (21, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  15. 15.In which quadrant does the point (8, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  17. 17.What is the midpoint of the line joining (9, 0) and (17, 6)? (a) (3, 13) (b) (26, 6) (c) (13, 3) (d) (4, 3)
  18. 18.In which quadrant does the point (9, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the distance between the points (0, 6) and (6, 14)? (a) 100 (b) 10 (c) 11 (d) 14
  20. 20.What is the distance between the points (0, 21) and (12, 5)? (a) 20 (b) 21 (c) 28 (d) 400
  21. 21.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.In which quadrant does the point (−4, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  23. 23.What is the midpoint of the line joining (2, 7) and (4, 15)? (a) (11, 3) (b) (6, 22) (c) (3, 11) (d) (1, 4)
  24. 24.What is the midpoint of the line joining (4, 8) and (16, 18)? (a) (20, 26) (b) (10, 13) (c) (6, 5) (d) (13, 10)
  25. 25.What is the distance between the points (7, 4) and (16, 16)? (a) 15 (b) 225 (c) 21 (d) 16
  26. 26.What is the midpoint of the line joining (4, 3) and (6, 11)? (a) (7, 5) (b) (1, 4) (c) (10, 14) (d) (5, 7)
  27. 27.In which quadrant does the point (−9, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (−5, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  29. 29.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  30. 30.What is the midpoint of the line joining (0, 5) and (6, 1)? (a) (4, 3) (b) (3, 3) (c) (6, 6) (d) (3, 2)
  31. 31.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  33. 33.What is the midpoint of the line joining (6, 5) and (8, 9)? (a) (7, 7) (b) (8, 7) (c) (14, 14) (d) (1, 2)
  34. 34.What is the midpoint of the line joining (2, 15) and (12, 7)? (a) (5, 4) (b) (7, 11) (c) (11, 7) (d) (14, 22)
  35. 35.What is the midpoint of the line joining (7, 4) and (17, 14)? (a) (12, 9) (b) (9, 12) (c) (5, 5) (d) (24, 18)
  36. 36.What is the distance between the points (1, 13) and (16, 5)? (a) 289 (b) 23 (c) 17 (d) 18
  37. 37.What is the distance between the points (6, 8) and (14, 2)? (a) 11 (b) 14 (c) 100 (d) 10
  38. 38.What is the distance between the points (3, 30) and (10, 6)? (a) 31 (b) 25 (c) 625 (d) 26
  39. 39.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10

Answer key

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

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