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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 779 · 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 (−1, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  4. 4.What is the distance between the points (7, 0) and (15, 6)? (a) 100 (b) 14 (c) 10 (d) 11
  5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  6. 6.What is the distance between the points (9, 4) and (15, 12)? (a) 14 (b) 100 (c) 10 (d) 11
  7. 7.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (0, 17) and (12, 1)? (a) 400 (b) 28 (c) 20 (d) 21
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  10. 10.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (2, 6) and (5, 2)? (a) 6 (b) 25 (c) 7 (d) 5
  12. 12.In which quadrant does the point (−8, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  13. 13.In which quadrant does the point (5, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  16. 16.What is the distance between the points (2, 6) and (10, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  17. 17.What is the distance between the points (4, 8) and (10, 16)? (a) 14 (b) 10 (c) 100 (d) 11
  18. 18.What is the midpoint of the line joining (0, 1) and (6, 3)? (a) (3, 2) (b) (2, 3) (c) (6, 4) (d) (3, 1)
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  20. 20.In which quadrant does the point (−5, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  21. 21.What is the midpoint of the line joining (9, 15) and (19, 7)? (a) (11, 14) (b) (28, 22) (c) (5, 4) (d) (14, 11)
  22. 22.What is the distance between the points (2, 4) and (9, 28)? (a) 26 (b) 31 (c) 625 (d) 25
  23. 23.What is the distance between the points (5, 18) and (17, 9)? (a) 21 (b) 15 (c) 16 (d) 225
  24. 24.What is the distance between the points (0, 1) and (24, 8)? (a) 625 (b) 31 (c) 26 (d) 25
  25. 25.In which quadrant does the point (−5, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  26. 26.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  27. 27.What is the midpoint of the line joining (2, 1) and (4, 5)? (a) (6, 6) (b) (4, 3) (c) (1, 2) (d) (3, 3)
  28. 28.What is the midpoint of the line joining (7, 14) and (15, 10)? (a) (12, 11) (b) (22, 24) (c) (11, 12) (d) (4, 2)
  29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  30. 30.In which quadrant does the point (−4, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the distance between the points (3, 30) and (10, 6)? (a) 31 (b) 625 (c) 25 (d) 26
  32. 32.What is the distance between the points (0, 2) and (6, 10)? (a) 100 (b) 11 (c) 14 (d) 10
  33. 33.What is the midpoint of the line joining (4, 8) and (6, 12)? (a) (10, 20) (b) (5, 10) (c) (1, 2) (d) (10, 5)
  34. 34.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  35. 35.What is the midpoint of the line joining (2, 2) and (12, 6)? (a) (5, 2) (b) (4, 7) (c) (7, 4) (d) (14, 8)
  36. 36.What is the distance between the points (5, 5) and (13, 11)? (a) 10 (b) 11 (c) 100 (d) 14
  37. 37.What is the distance between the points (7, 1) and (10, 5)? (a) 6 (b) 5 (c) 7 (d) 25
  38. 38.What is the distance between the points (0, 8) and (6, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  39. 39.What is the midpoint of the line joining (9, 17) and (17, 7)? (a) (4, 5) (b) (12, 13) (c) (13, 12) (d) (26, 24)
  40. 40.What is the midpoint of the line joining (3, 8) and (11, 14)? (a) (4, 3) (b) (11, 7) (c) (14, 22) (d) (7, 11)

Answer key

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

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