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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 229 · 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 (8, 1) and (23, 9)? (a) 289 (b) 17 (c) 18 (d) 23
  2. 2.In which quadrant does the point (−5, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  3. 3.What is the distance between the points (8, 8) and (20, 3)? (a) 13 (b) 169 (c) 17 (d) 14
  4. 4.What is the distance between the points (4, 7) and (16, 12)? (a) 17 (b) 14 (c) 169 (d) 13
  5. 5.What is the distance between the points (2, 3) and (10, 9)? (a) 100 (b) 10 (c) 11 (d) 14
  6. 6.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  8. 8.What is the midpoint of the line joining (1, 16) and (3, 10)? (a) (2, 13) (b) (13, 2) (c) (4, 26) (d) (1, 3)
  9. 9.What is the distance between the points (4, 3) and (10, 11)? (a) 14 (b) 100 (c) 11 (d) 10
  10. 10.What is the distance between the points (8, 16) and (14, 8)? (a) 14 (b) 100 (c) 10 (d) 11
  11. 11.What is the distance between the points (7, 17) and (19, 8)? (a) 16 (b) 21 (c) 225 (d) 15
  12. 12.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  13. 13.What is the distance between the points (0, 9) and (8, 24)? (a) 23 (b) 17 (c) 289 (d) 18
  14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  17. 17.What is the distance between the points (1, 5) and (16, 13)? (a) 17 (b) 18 (c) 289 (d) 23
  18. 18.What is the distance between the points (6, 6) and (10, 3)? (a) 25 (b) 5 (c) 7 (d) 6
  19. 19.What is the midpoint of the line joining (8, 5) and (14, 7)? (a) (3, 1) (b) (11, 6) (c) (6, 11) (d) (22, 12)
  20. 20.What is the distance between the points (5, 9) and (17, 14)? (a) 17 (b) 13 (c) 169 (d) 14
  21. 21.What is the distance between the points (0, 7) and (6, 15)? (a) 10 (b) 11 (c) 100 (d) 14
  22. 22.What is the distance between the points (0, 8) and (15, 16)? (a) 23 (b) 18 (c) 289 (d) 17
  23. 23.In which quadrant does the point (−1, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  24. 24.In which quadrant does the point (3, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  26. 26.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  27. 27.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  28. 28.What is the midpoint of the line joining (2, 9) and (4, 13)? (a) (1, 2) (b) (3, 11) (c) (6, 22) (d) (11, 3)
  29. 29.In which quadrant does the point (−6, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  30. 30.In which quadrant does the point (−6, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  31. 31.What is the distance between the points (6, 2) and (14, 8)? (a) 14 (b) 10 (c) 100 (d) 11
  32. 32.What is the midpoint of the line joining (8, 0) and (20, 4)? (a) (28, 4) (b) (2, 14) (c) (14, 2) (d) (6, 2)
  33. 33.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.What is the midpoint of the line joining (8, 12) and (16, 4)? (a) (4, 4) (b) (12, 8) (c) (8, 12) (d) (24, 16)
  35. 35.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  37. 37.What is the midpoint of the line joining (9, 6) and (19, 0)? (a) (3, 14) (b) (5, 3) (c) (28, 6) (d) (14, 3)
  38. 38.What is the distance between the points (4, 12) and (16, 3)? (a) 225 (b) 16 (c) 15 (d) 21
  39. 39.What is the midpoint of the line joining (7, 5) and (19, 9)? (a) (7, 13) (b) (13, 7) (c) (6, 2) (d) (26, 14)
  40. 40.In which quadrant does the point (4, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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