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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 143 · 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.In which quadrant does the point (8, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.What is the midpoint of the line joining (8, 10) and (10, 18)? (a) (14, 9) (b) (18, 28) (c) (9, 14) (d) (1, 4)
  3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  4. 4.In which quadrant does the point (4, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  5. 5.In which quadrant does the point (9, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  6. 6.In which quadrant does the point (−3, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.In which quadrant does the point (−1, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  8. 8.What is the distance between the points (3, 13) and (9, 5)? (a) 10 (b) 14 (c) 100 (d) 11
  9. 9.What is the midpoint of the line joining (1, 14) and (11, 4)? (a) (9, 6) (b) (12, 18) (c) (6, 9) (d) (5, 5)
  10. 10.What is the distance between the points (7, 9) and (11, 12)? (a) 25 (b) 7 (c) 6 (d) 5
  11. 11.What is the distance between the points (3, 8) and (15, 17)? (a) 21 (b) 225 (c) 15 (d) 16
  12. 12.What is the distance between the points (4, 9) and (16, 18)? (a) 16 (b) 15 (c) 21 (d) 225
  13. 13.What is the midpoint of the line joining (5, 8) and (11, 14)? (a) (8, 11) (b) (11, 8) (c) (16, 22) (d) (3, 3)
  14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  15. 15.What is the midpoint of the line joining (7, 6) and (19, 8)? (a) (6, 1) (b) (13, 7) (c) (7, 13) (d) (26, 14)
  16. 16.What is the midpoint of the line joining (7, 5) and (9, 13)? (a) (16, 18) (b) (1, 4) (c) (9, 8) (d) (8, 9)
  17. 17.In which quadrant does the point (−5, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the midpoint of the line joining (0, 2) and (6, 4)? (a) (3, 1) (b) (4, 3) (c) (3, 3) (d) (6, 6)
  19. 19.In which quadrant does the point (5, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the distance between the points (8, 3) and (20, 19)? (a) 400 (b) 20 (c) 28 (d) 21
  21. 21.In which quadrant does the point (2, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.What is the distance between the points (9, 9) and (33, 2)? (a) 26 (b) 625 (c) 25 (d) 31
  23. 23.What is the distance between the points (6, 6) and (21, 14)? (a) 17 (b) 23 (c) 18 (d) 289
  24. 24.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (0, 1) and (4, 11)? (a) (2, 6) (b) (6, 2) (c) (4, 12) (d) (2, 5)
  26. 26.What is the distance between the points (6, 1) and (18, 17)? (a) 28 (b) 21 (c) 20 (d) 400
  27. 27.What is the distance between the points (0, 2) and (5, 14)? (a) 17 (b) 13 (c) 169 (d) 14
  28. 28.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.What is the midpoint of the line joining (1, 4) and (11, 16)? (a) (5, 6) (b) (6, 10) (c) (12, 20) (d) (10, 6)
  30. 30.In which quadrant does the point (−8, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  31. 31.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  32. 32.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  33. 33.What is the distance between the points (9, 10) and (24, 2)? (a) 23 (b) 18 (c) 17 (d) 289
  34. 34.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  36. 36.What is the midpoint of the line joining (5, 4) and (17, 0)? (a) (2, 11) (b) (6, 2) (c) (22, 4) (d) (11, 2)
  37. 37.What is the distance between the points (5, 27) and (12, 3)? (a) 31 (b) 625 (c) 26 (d) 25
  38. 38.In which quadrant does the point (−6, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (4, 1) and (14, 3)? (a) (5, 1) (b) (9, 2) (c) (2, 9) (d) (18, 4)
  40. 40.In which quadrant does the point (−7, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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