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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 512 · 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 (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  2. 2.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.In which quadrant does the point (−2, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  5. 5.What is the distance between the points (1, 3) and (8, 27)? (a) 26 (b) 25 (c) 31 (d) 625
  6. 6.In which quadrant does the point (−3, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  7. 7.In which quadrant does the point (−2, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  8. 8.What is the distance between the points (1, 2) and (6, 14)? (a) 14 (b) 13 (c) 169 (d) 17
  9. 9.What is the midpoint of the line joining (2, 4) and (6, 12)? (a) (2, 4) (b) (4, 8) (c) (8, 4) (d) (8, 16)
  10. 10.What is the midpoint of the line joining (9, 10) and (13, 12)? (a) (2, 1) (b) (22, 22) (c) (12, 11) (d) (11, 11)
  11. 11.What is the distance between the points (1, 5) and (13, 14)? (a) 15 (b) 21 (c) 16 (d) 225
  12. 12.What is the midpoint of the line joining (9, 12) and (17, 10)? (a) (13, 11) (b) (26, 22) (c) (4, 1) (d) (11, 13)
  13. 13.What is the distance between the points (1, 3) and (13, 19)? (a) 21 (b) 20 (c) 28 (d) 400
  14. 14.In which quadrant does the point (−8, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  15. 15.What is the distance between the points (4, 9) and (8, 12)? (a) 7 (b) 6 (c) 25 (d) 5
  16. 16.What is the distance between the points (9, 12) and (14, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  17. 17.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  18. 18.What is the distance between the points (2, 11) and (8, 3)? (a) 11 (b) 10 (c) 100 (d) 14
  19. 19.In which quadrant does the point (4, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  20. 20.In which quadrant does the point (9, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  22. 22.What is the distance between the points (5, 1) and (29, 8)? (a) 31 (b) 625 (c) 26 (d) 25
  23. 23.What is the midpoint of the line joining (3, 4) and (11, 6)? (a) (14, 10) (b) (5, 7) (c) (7, 5) (d) (4, 1)
  24. 24.What is the midpoint of the line joining (2, 10) and (8, 12)? (a) (5, 11) (b) (3, 1) (c) (11, 5) (d) (10, 22)
  25. 25.What is the distance between the points (0, 11) and (8, 5)? (a) 14 (b) 100 (c) 10 (d) 11
  26. 26.What is the midpoint of the line joining (9, 12) and (13, 6)? (a) (22, 18) (b) (2, 3) (c) (11, 9) (d) (9, 11)
  27. 27.What is the midpoint of the line joining (6, 10) and (12, 16)? (a) (13, 9) (b) (9, 13) (c) (3, 3) (d) (18, 26)
  28. 28.In which quadrant does the point (−9, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  29. 29.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  30. 30.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  31. 31.What is the distance between the points (1, 17) and (16, 9)? (a) 23 (b) 289 (c) 17 (d) 18
  32. 32.What is the midpoint of the line joining (6, 0) and (10, 2)? (a) (1, 8) (b) (2, 1) (c) (8, 1) (d) (16, 2)
  33. 33.What is the midpoint of the line joining (2, 6) and (4, 8)? (a) (7, 3) (b) (3, 7) (c) (1, 1) (d) (6, 14)
  34. 34.What is the distance between the points (2, 2) and (26, 9)? (a) 625 (b) 25 (c) 26 (d) 31
  35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  36. 36.In which quadrant does the point (5, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  37. 37.What is the distance between the points (3, 1) and (7, 4)? (a) 5 (b) 25 (c) 6 (d) 7
  38. 38.What is the midpoint of the line joining (1, 4) and (7, 0)? (a) (2, 4) (b) (4, 2) (c) (8, 4) (d) (3, 2)
  39. 39.What is the distance between the points (0, 1) and (4, 4)? (a) 25 (b) 7 (c) 5 (d) 6
  40. 40.What is the midpoint of the line joining (3, 13) and (7, 3)? (a) (2, 5) (b) (5, 8) (c) (8, 5) (d) (10, 16)

Answer key

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

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