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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 665 · 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 distance between the points (9, 7) and (12, 3)? (a) 25 (b) 7 (c) 6 (d) 5
  2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  3. 3.What is the distance between the points (4, 13) and (28, 6)? (a) 625 (b) 26 (c) 25 (d) 31
  4. 4.In which quadrant does the point (8, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  5. 5.What is the midpoint of the line joining (0, 7) and (12, 13)? (a) (6, 3) (b) (12, 20) (c) (6, 10) (d) (10, 6)
  6. 6.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  8. 8.What is the distance between the points (8, 20) and (13, 8)? (a) 13 (b) 17 (c) 14 (d) 169
  9. 9.What is the midpoint of the line joining (0, 1) and (8, 3)? (a) (8, 4) (b) (4, 1) (c) (4, 2) (d) (2, 4)
  10. 10.What is the midpoint of the line joining (8, 9) and (14, 1)? (a) (11, 5) (b) (5, 11) (c) (22, 10) (d) (3, 4)
  11. 11.In which quadrant does the point (−3, 7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  13. 13.What is the distance between the points (4, 11) and (16, 2)? (a) 15 (b) 225 (c) 16 (d) 21
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  15. 15.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  16. 16.What is the midpoint of the line joining (4, 3) and (14, 9)? (a) (5, 3) (b) (9, 6) (c) (6, 9) (d) (18, 12)
  17. 17.In which quadrant does the point (1, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  20. 20.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  21. 21.What is the distance between the points (9, 7) and (21, 16)? (a) 16 (b) 21 (c) 15 (d) 225
  22. 22.In which quadrant does the point (−3, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  24. 24.What is the midpoint of the line joining (2, 1) and (4, 13)? (a) (6, 14) (b) (7, 3) (c) (1, 6) (d) (3, 7)
  25. 25.What is the midpoint of the line joining (9, 12) and (13, 2)? (a) (2, 5) (b) (22, 14) (c) (7, 11) (d) (11, 7)
  26. 26.In which quadrant does the point (4, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  28. 28.In which quadrant does the point (5, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.What is the distance between the points (8, 3) and (11, 7)? (a) 5 (b) 25 (c) 6 (d) 7
  30. 30.What is the midpoint of the line joining (5, 8) and (15, 14)? (a) (5, 3) (b) (10, 11) (c) (20, 22) (d) (11, 10)
  31. 31.In which quadrant does the point (9, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  32. 32.What is the distance between the points (5, 18) and (10, 6)? (a) 17 (b) 169 (c) 13 (d) 14
  33. 33.What is the midpoint of the line joining (0, 0) and (6, 12)? (a) (3, 6) (b) (6, 12) (c) (4, 6) (d) (6, 3)
  34. 34.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the distance between the points (4, 2) and (12, 17)? (a) 289 (b) 17 (c) 23 (d) 18
  36. 36.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (3, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  38. 38.What is the distance between the points (0, 6) and (3, 2)? (a) 7 (b) 6 (c) 25 (d) 5
  39. 39.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  40. 40.What is the distance between the points (3, 7) and (10, 31)? (a) 31 (b) 625 (c) 25 (d) 26

Answer key

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

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