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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 828 · 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.In which quadrant does the point (2, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  3. 3.What is the midpoint of the line joining (10, 11) and (12, 1)? (a) (6, 11) (b) (11, 6) (c) (1, 5) (d) (22, 12)
  4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  5. 5.What is the distance between the points (7, 12) and (13, 4)? (a) 100 (b) 10 (c) 11 (d) 14
  6. 6.What is the distance between the points (1, 8) and (9, 23)? (a) 289 (b) 18 (c) 23 (d) 17
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  8. 8.What is the midpoint of the line joining (3, 3) and (5, 5)? (a) (8, 8) (b) (1, 1) (c) (4, 4) (d) (5, 4)
  9. 9.What is the distance between the points (5, 9) and (10, 21)? (a) 13 (b) 17 (c) 14 (d) 169
  10. 10.What is the midpoint of the line joining (7, 7) and (11, 19)? (a) (13, 9) (b) (2, 6) (c) (9, 13) (d) (18, 26)
  11. 11.What is the distance between the points (5, 5) and (9, 2)? (a) 25 (b) 5 (c) 7 (d) 6
  12. 12.What is the distance between the points (1, 5) and (16, 13)? (a) 289 (b) 18 (c) 23 (d) 17
  13. 13.In which quadrant does the point (6, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (7, 0) and (11, 2)? (a) (2, 1) (b) (9, 1) (c) (1, 9) (d) (18, 2)
  15. 15.What is the midpoint of the line joining (6, 18) and (10, 8)? (a) (2, 5) (b) (16, 26) (c) (13, 8) (d) (8, 13)
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  17. 17.What is the distance between the points (1, 15) and (7, 7)? (a) 100 (b) 10 (c) 11 (d) 14
  18. 18.What is the midpoint of the line joining (4, 14) and (12, 2)? (a) (16, 16) (b) (9, 8) (c) (4, 6) (d) (8, 8)
  19. 19.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  20. 20.What is the midpoint of the line joining (9, 9) and (21, 13)? (a) (30, 22) (b) (6, 2) (c) (15, 11) (d) (11, 15)
  21. 21.In which quadrant does the point (5, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.In which quadrant does the point (9, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  23. 23.What is the midpoint of the line joining (10, 11) and (16, 9)? (a) (13, 10) (b) (26, 20) (c) (3, 1) (d) (10, 13)
  24. 24.What is the midpoint of the line joining (6, 4) and (8, 14)? (a) (1, 5) (b) (9, 7) (c) (14, 18) (d) (7, 9)
  25. 25.What is the midpoint of the line joining (1, 14) and (11, 8)? (a) (5, 3) (b) (12, 22) (c) (11, 6) (d) (6, 11)
  26. 26.In which quadrant does the point (−3, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  29. 29.In which quadrant does the point (2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  30. 30.What is the distance between the points (9, 14) and (33, 7)? (a) 25 (b) 26 (c) 31 (d) 625
  31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  32. 32.What is the distance between the points (3, 13) and (18, 5)? (a) 17 (b) 289 (c) 18 (d) 23
  33. 33.In which quadrant does the point (−9, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  34. 34.In which quadrant does the point (−5, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  35. 35.What is the distance between the points (2, 12) and (8, 4)? (a) 11 (b) 10 (c) 14 (d) 100
  36. 36.What is the distance between the points (3, 4) and (7, 1)? (a) 6 (b) 7 (c) 25 (d) 5
  37. 37.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  38. 38.What is the midpoint of the line joining (10, 5) and (14, 9)? (a) (2, 2) (b) (12, 7) (c) (7, 12) (d) (24, 14)
  39. 39.What is the distance between the points (0, 6) and (16, 18)? (a) 400 (b) 20 (c) 28 (d) 21
  40. 40.What is the distance between the points (7, 11) and (22, 3)? (a) 18 (b) 17 (c) 289 (d) 23

Answer key

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

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