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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 662 · 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 (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  2. 2.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  3. 3.In which quadrant does the point (−4, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  4. 4.What is the distance between the points (4, 24) and (12, 9)? (a) 289 (b) 23 (c) 18 (d) 17
  5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  7. 7.What is the distance between the points (9, 2) and (13, 5)? (a) 25 (b) 5 (c) 6 (d) 7
  8. 8.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  9. 9.What is the distance between the points (7, 7) and (10, 3)? (a) 6 (b) 7 (c) 5 (d) 25
  10. 10.In which quadrant does the point (−6, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  11. 11.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  12. 12.In which quadrant does the point (−2, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  13. 13.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  14. 14.In which quadrant does the point (7, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  15. 15.What is the midpoint of the line joining (3, 8) and (13, 18)? (a) (16, 26) (b) (5, 5) (c) (13, 8) (d) (8, 13)
  16. 16.What is the midpoint of the line joining (6, 8) and (12, 18)? (a) (3, 5) (b) (18, 26) (c) (13, 9) (d) (9, 13)
  17. 17.What is the midpoint of the line joining (4, 14) and (6, 10)? (a) (1, 2) (b) (10, 24) (c) (5, 12) (d) (12, 5)
  18. 18.In which quadrant does the point (8, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (9, 9) and (13, 5)? (a) (22, 14) (b) (2, 2) (c) (11, 7) (d) (7, 11)
  20. 20.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  21. 21.What is the midpoint of the line joining (3, 4) and (7, 2)? (a) (10, 6) (b) (2, 1) (c) (3, 5) (d) (5, 3)
  22. 22.In which quadrant does the point (−7, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  23. 23.What is the distance between the points (8, 1) and (20, 6)? (a) 13 (b) 169 (c) 14 (d) 17
  24. 24.What is the distance between the points (1, 5) and (13, 14)? (a) 225 (b) 16 (c) 15 (d) 21
  25. 25.What is the midpoint of the line joining (7, 13) and (11, 3)? (a) (8, 9) (b) (2, 5) (c) (9, 8) (d) (18, 16)
  26. 26.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.In which quadrant does the point (−4, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (7, 4) and (13, 8)? (a) (6, 10) (b) (20, 12) (c) (10, 6) (d) (3, 2)
  29. 29.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  30. 30.In which quadrant does the point (1, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  31. 31.What is the midpoint of the line joining (2, 5) and (10, 1)? (a) (4, 2) (b) (6, 3) (c) (3, 6) (d) (12, 6)
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  33. 33.In which quadrant does the point (2, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.What is the distance between the points (0, 6) and (15, 14)? (a) 23 (b) 18 (c) 289 (d) 17
  35. 35.What is the midpoint of the line joining (10, 6) and (20, 10)? (a) (5, 2) (b) (8, 15) (c) (30, 16) (d) (15, 8)
  36. 36.In which quadrant does the point (3, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.In which quadrant does the point (8, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the midpoint of the line joining (10, 12) and (16, 2)? (a) (7, 13) (b) (13, 7) (c) (3, 5) (d) (26, 14)
  39. 39.What is the midpoint of the line joining (3, 7) and (7, 5)? (a) (6, 5) (b) (2, 1) (c) (10, 12) (d) (5, 6)
  40. 40.What is the midpoint of the line joining (6, 3) and (10, 7)? (a) (2, 2) (b) (8, 5) (c) (16, 10) (d) (5, 8)

Answer key

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

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