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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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