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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 427 · 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 (1, 26) and (8, 2)? (a) 625 (b) 26 (c) 31 (d) 25
  2. 2.What is the distance between the points (5, 0) and (29, 7)? (a) 625 (b) 31 (c) 26 (d) 25
  3. 3.What is the distance between the points (1, 7) and (4, 11)? (a) 7 (b) 5 (c) 25 (d) 6
  4. 4.In which quadrant does the point (1, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  5. 5.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  6. 6.What is the distance between the points (9, 3) and (17, 18)? (a) 18 (b) 289 (c) 17 (d) 23
  7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  8. 8.In which quadrant does the point (2, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  10. 10.What is the distance between the points (8, 1) and (20, 17)? (a) 28 (b) 20 (c) 400 (d) 21
  11. 11.What is the distance between the points (9, 3) and (24, 11)? (a) 18 (b) 23 (c) 289 (d) 17
  12. 12.In which quadrant does the point (6, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.What is the distance between the points (1, 15) and (9, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  14. 14.In which quadrant does the point (−2, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (7, 7) and (19, 12)? (a) 169 (b) 14 (c) 13 (d) 17
  16. 16.What is the midpoint of the line joining (8, 10) and (10, 14)? (a) (12, 9) (b) (18, 24) (c) (9, 12) (d) (1, 2)
  17. 17.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  19. 19.What is the distance between the points (0, 12) and (9, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  20. 20.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  22. 22.In which quadrant does the point (6, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  23. 23.What is the distance between the points (8, 13) and (20, 4)? (a) 21 (b) 225 (c) 15 (d) 16
  24. 24.What is the midpoint of the line joining (2, 5) and (4, 7)? (a) (6, 3) (b) (6, 12) (c) (3, 6) (d) (1, 1)
  25. 25.What is the distance between the points (2, 0) and (10, 15)? (a) 289 (b) 18 (c) 23 (d) 17
  26. 26.In which quadrant does the point (−8, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  28. 28.What is the distance between the points (7, 12) and (19, 3)? (a) 15 (b) 21 (c) 225 (d) 16
  29. 29.What is the distance between the points (4, 7) and (12, 13)? (a) 11 (b) 14 (c) 100 (d) 10
  30. 30.In which quadrant does the point (−8, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  32. 32.In which quadrant does the point (7, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  34. 34.What is the distance between the points (6, 1) and (9, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  35. 35.In which quadrant does the point (−4, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (9, 8) and (11, 12)? (a) (20, 20) (b) (10, 10) (c) (1, 2) (d) (11, 10)
  37. 37.What is the midpoint of the line joining (10, 1) and (12, 13)? (a) (22, 14) (b) (11, 7) (c) (7, 11) (d) (1, 6)
  38. 38.In which quadrant does the point (9, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (9, 11) and (15, 7)? (a) (9, 12) (b) (12, 9) (c) (24, 18) (d) (3, 2)
  40. 40.What is the distance between the points (7, 3) and (13, 11)? (a) 10 (b) 14 (c) 11 (d) 100

Answer key

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

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