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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 144 · 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, 10) and (12, 2)? (a) (3, 4) (b) (18, 12) (c) (9, 6) (d) (6, 9)
  2. 2.What is the distance between the points (7, 5) and (31, 12)? (a) 31 (b) 625 (c) 26 (d) 25
  3. 3.What is the midpoint of the line joining (3, 1) and (9, 3)? (a) (6, 2) (b) (3, 1) (c) (12, 4) (d) (2, 6)
  4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  5. 5.What is the midpoint of the line joining (1, 12) and (3, 6)? (a) (2, 9) (b) (9, 2) (c) (4, 18) (d) (1, 3)
  6. 6.What is the distance between the points (7, 6) and (16, 18)? (a) 21 (b) 16 (c) 225 (d) 15
  7. 7.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  8. 8.What is the distance between the points (9, 1) and (17, 7)? (a) 100 (b) 11 (c) 10 (d) 14
  9. 9.What is the midpoint of the line joining (6, 10) and (12, 6)? (a) (3, 2) (b) (18, 16) (c) (9, 8) (d) (8, 9)
  10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  12. 12.What is the distance between the points (4, 8) and (9, 20)? (a) 14 (b) 13 (c) 169 (d) 17
  13. 13.In which quadrant does the point (5, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  14. 14.What is the distance between the points (9, 11) and (12, 7)? (a) 6 (b) 25 (c) 7 (d) 5
  15. 15.What is the midpoint of the line joining (10, 10) and (16, 8)? (a) (9, 13) (b) (13, 9) (c) (26, 18) (d) (3, 1)
  16. 16.What is the midpoint of the line joining (0, 2) and (10, 6)? (a) (4, 5) (b) (5, 2) (c) (10, 8) (d) (5, 4)
  17. 17.In which quadrant does the point (8, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  19. 19.What is the distance between the points (3, 15) and (15, 6)? (a) 16 (b) 15 (c) 21 (d) 225
  20. 20.In which quadrant does the point (−6, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.What is the midpoint of the line joining (4, 12) and (8, 4)? (a) (12, 16) (b) (2, 4) (c) (6, 8) (d) (8, 6)
  22. 22.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  23. 23.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  24. 24.In which quadrant does the point (6, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (3, 23) and (11, 8)? (a) 23 (b) 289 (c) 18 (d) 17
  26. 26.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  27. 27.What is the distance between the points (1, 11) and (5, 8)? (a) 5 (b) 6 (c) 25 (d) 7
  28. 28.What is the distance between the points (7, 14) and (15, 8)? (a) 14 (b) 10 (c) 11 (d) 100
  29. 29.In which quadrant does the point (8, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  30. 30.What is the midpoint of the line joining (1, 12) and (5, 2)? (a) (2, 5) (b) (3, 7) (c) (7, 3) (d) (6, 14)
  31. 31.What is the midpoint of the line joining (0, 10) and (8, 16)? (a) (4, 3) (b) (4, 13) (c) (8, 26) (d) (13, 4)
  32. 32.In which quadrant does the point (9, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (−5, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (1, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  36. 36.What is the distance between the points (1, 19) and (13, 3)? (a) 20 (b) 400 (c) 28 (d) 21
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  38. 38.What is the distance between the points (1, 3) and (4, 7)? (a) 6 (b) 5 (c) 25 (d) 7
  39. 39.In which quadrant does the point (2, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  40. 40.In which quadrant does the point (1, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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