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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 128 · 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 (−8, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  2. 2.What is the midpoint of the line joining (6, 4) and (10, 2)? (a) (2, 1) (b) (8, 3) (c) (3, 8) (d) (16, 6)
  3. 3.What is the distance between the points (7, 10) and (13, 2)? (a) 14 (b) 11 (c) 100 (d) 10
  4. 4.What is the distance between the points (7, 12) and (10, 8)? (a) 5 (b) 6 (c) 25 (d) 7
  5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  6. 6.What is the midpoint of the line joining (6, 4) and (16, 8)? (a) (22, 12) (b) (5, 2) (c) (11, 6) (d) (6, 11)
  7. 7.What is the distance between the points (1, 20) and (13, 4)? (a) 400 (b) 20 (c) 28 (d) 21
  8. 8.What is the midpoint of the line joining (8, 7) and (16, 17)? (a) (13, 12) (b) (4, 5) (c) (12, 12) (d) (24, 24)
  9. 9.What is the distance between the points (0, 3) and (9, 15)? (a) 15 (b) 16 (c) 21 (d) 225
  10. 10.What is the distance between the points (3, 12) and (12, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  11. 11.What is the distance between the points (5, 15) and (20, 7)? (a) 289 (b) 18 (c) 23 (d) 17
  12. 12.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  14. 14.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  15. 15.What is the midpoint of the line joining (2, 19) and (6, 7)? (a) (13, 4) (b) (4, 13) (c) (8, 26) (d) (2, 6)
  16. 16.In which quadrant does the point (8, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  17. 17.What is the distance between the points (1, 3) and (13, 19)? (a) 20 (b) 28 (c) 21 (d) 400
  18. 18.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  19. 19.What is the distance between the points (6, 2) and (9, 6)? (a) 6 (b) 5 (c) 7 (d) 25
  20. 20.What is the distance between the points (7, 20) and (12, 8)? (a) 14 (b) 169 (c) 13 (d) 17
  21. 21.In which quadrant does the point (7, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  23. 23.What is the distance between the points (3, 2) and (18, 10)? (a) 18 (b) 23 (c) 289 (d) 17
  24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  25. 25.What is the distance between the points (2, 3) and (17, 11)? (a) 18 (b) 23 (c) 17 (d) 289
  26. 26.What is the distance between the points (1, 7) and (6, 19)? (a) 169 (b) 13 (c) 17 (d) 14
  27. 27.What is the distance between the points (1, 7) and (10, 19)? (a) 21 (b) 225 (c) 16 (d) 15
  28. 28.What is the distance between the points (8, 7) and (14, 15)? (a) 11 (b) 14 (c) 100 (d) 10
  29. 29.In which quadrant does the point (−2, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  30. 30.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  31. 31.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  32. 32.What is the distance between the points (6, 4) and (9, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  33. 33.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  34. 34.What is the distance between the points (0, 1) and (8, 7)? (a) 10 (b) 11 (c) 100 (d) 14
  35. 35.What is the midpoint of the line joining (1, 2) and (9, 4)? (a) (10, 6) (b) (4, 1) (c) (3, 5) (d) (5, 3)
  36. 36.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  38. 38.What is the distance between the points (9, 4) and (21, 9)? (a) 13 (b) 14 (c) 169 (d) 17
  39. 39.In which quadrant does the point (−8, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (3, 8) and (27, 15)? (a) 26 (b) 625 (c) 31 (d) 25

Answer key

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

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