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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 87 · 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 (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  4. 4.In which quadrant does the point (−2, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  5. 5.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  6. 6.What is the midpoint of the line joining (7, 2) and (13, 4)? (a) (3, 1) (b) (3, 10) (c) (20, 6) (d) (10, 3)
  7. 7.What is the distance between the points (2, 6) and (18, 18)? (a) 21 (b) 20 (c) 28 (d) 400
  8. 8.In which quadrant does the point (−3, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (1, 6) and (25, 13)? (a) 25 (b) 26 (c) 625 (d) 31
  10. 10.In which quadrant does the point (1, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  11. 11.What is the midpoint of the line joining (1, 14) and (9, 8)? (a) (10, 22) (b) (11, 5) (c) (5, 11) (d) (4, 3)
  12. 12.In which quadrant does the point (4, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  13. 13.In which quadrant does the point (−7, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  14. 14.What is the distance between the points (3, 9) and (9, 1)? (a) 11 (b) 100 (c) 14 (d) 10
  15. 15.What is the distance between the points (3, 8) and (10, 32)? (a) 25 (b) 625 (c) 26 (d) 31
  16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  17. 17.What is the distance between the points (9, 13) and (33, 6)? (a) 25 (b) 625 (c) 31 (d) 26
  18. 18.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  19. 19.What is the distance between the points (0, 15) and (8, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  20. 20.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  21. 21.What is the midpoint of the line joining (8, 9) and (20, 13)? (a) (28, 22) (b) (11, 14) (c) (14, 11) (d) (6, 2)
  22. 22.What is the distance between the points (5, 9) and (21, 21)? (a) 400 (b) 21 (c) 20 (d) 28
  23. 23.What is the distance between the points (1, 19) and (9, 4)? (a) 18 (b) 17 (c) 289 (d) 23
  24. 24.What is the midpoint of the line joining (6, 1) and (14, 3)? (a) (20, 4) (b) (2, 10) (c) (10, 2) (d) (4, 1)
  25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  26. 26.What is the midpoint of the line joining (9, 8) and (13, 2)? (a) (11, 5) (b) (5, 11) (c) (22, 10) (d) (2, 3)
  27. 27.In which quadrant does the point (−3, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  28. 28.What is the distance between the points (9, 1) and (25, 13)? (a) 400 (b) 21 (c) 20 (d) 28
  29. 29.In which quadrant does the point (−8, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  30. 30.In which quadrant does the point (−8, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  33. 33.What is the distance between the points (2, 7) and (5, 3)? (a) 25 (b) 7 (c) 6 (d) 5
  34. 34.What is the midpoint of the line joining (8, 10) and (16, 2)? (a) (12, 6) (b) (4, 4) (c) (24, 12) (d) (6, 12)
  35. 35.What is the distance between the points (9, 6) and (14, 18)? (a) 17 (b) 169 (c) 14 (d) 13
  36. 36.What is the distance between the points (0, 8) and (7, 32)? (a) 25 (b) 625 (c) 26 (d) 31
  37. 37.In which quadrant does the point (8, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the midpoint of the line joining (2, 8) and (12, 12)? (a) (14, 20) (b) (5, 2) (c) (7, 10) (d) (10, 7)
  39. 39.In which quadrant does the point (7, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  40. 40.In which quadrant does the point (5, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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