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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 110 · 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 (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  3. 3.What is the midpoint of the line joining (10, 7) and (22, 9)? (a) (8, 16) (b) (16, 8) (c) (6, 1) (d) (32, 16)
  4. 4.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  6. 6.What is the distance between the points (8, 21) and (17, 9)? (a) 16 (b) 21 (c) 15 (d) 225
  7. 7.What is the distance between the points (8, 0) and (12, 3)? (a) 5 (b) 7 (c) 6 (d) 25
  8. 8.What is the midpoint of the line joining (8, 7) and (14, 3)? (a) (3, 2) (b) (22, 10) (c) (11, 5) (d) (5, 11)
  9. 9.What is the distance between the points (8, 14) and (20, 5)? (a) 21 (b) 16 (c) 15 (d) 225
  10. 10.What is the midpoint of the line joining (5, 10) and (15, 22)? (a) (10, 16) (b) (5, 6) (c) (20, 32) (d) (16, 10)
  11. 11.What is the distance between the points (6, 16) and (12, 8)? (a) 100 (b) 14 (c) 10 (d) 11
  12. 12.In which quadrant does the point (4, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  13. 13.In which quadrant does the point (−5, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  14. 14.What is the distance between the points (3, 18) and (12, 6)? (a) 21 (b) 16 (c) 225 (d) 15
  15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  16. 16.What is the midpoint of the line joining (1, 11) and (5, 9)? (a) (6, 20) (b) (2, 1) (c) (3, 10) (d) (10, 3)
  17. 17.What is the distance between the points (3, 15) and (12, 3)? (a) 15 (b) 16 (c) 21 (d) 225
  18. 18.What is the midpoint of the line joining (10, 9) and (16, 1)? (a) (5, 13) (b) (3, 4) (c) (13, 5) (d) (26, 10)
  19. 19.In which quadrant does the point (7, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  21. 21.What is the distance between the points (2, 0) and (7, 12)? (a) 13 (b) 17 (c) 169 (d) 14
  22. 22.What is the midpoint of the line joining (6, 14) and (12, 10)? (a) (3, 2) (b) (12, 9) (c) (18, 24) (d) (9, 12)
  23. 23.What is the midpoint of the line joining (3, 8) and (15, 18)? (a) (18, 26) (b) (9, 13) (c) (13, 9) (d) (6, 5)
  24. 24.What is the distance between the points (8, 15) and (23, 7)? (a) 289 (b) 18 (c) 23 (d) 17
  25. 25.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  26. 26.What is the midpoint of the line joining (7, 12) and (11, 2)? (a) (18, 14) (b) (7, 9) (c) (9, 7) (d) (2, 5)
  27. 27.What is the distance between the points (0, 1) and (3, 5)? (a) 7 (b) 5 (c) 25 (d) 6
  28. 28.In which quadrant does the point (5, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (4, 7) and (12, 13)? (a) 10 (b) 100 (c) 11 (d) 14
  30. 30.What is the distance between the points (2, 5) and (9, 29)? (a) 25 (b) 26 (c) 31 (d) 625
  31. 31.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  33. 33.What is the distance between the points (8, 4) and (32, 11)? (a) 31 (b) 25 (c) 625 (d) 26
  34. 34.In which quadrant does the point (−8, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  35. 35.What is the midpoint of the line joining (7, 5) and (11, 9)? (a) (2, 2) (b) (9, 7) (c) (7, 9) (d) (18, 14)
  36. 36.In which quadrant does the point (6, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  37. 37.What is the distance between the points (5, 12) and (10, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  38. 38.What is the distance between the points (2, 14) and (11, 2)? (a) 16 (b) 225 (c) 21 (d) 15
  39. 39.What is the midpoint of the line joining (7, 8) and (13, 10)? (a) (3, 1) (b) (10, 9) (c) (9, 10) (d) (20, 18)
  40. 40.What is the midpoint of the line joining (5, 2) and (17, 10)? (a) (6, 11) (b) (6, 4) (c) (22, 12) (d) (11, 6)

Answer key

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

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