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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 382 · 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 (5, 3) and (14, 15)? (a) 225 (b) 21 (c) 16 (d) 15
  2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  3. 3.What is the distance between the points (2, 1) and (9, 25)? (a) 26 (b) 625 (c) 31 (d) 25
  4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  5. 5.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.What is the midpoint of the line joining (9, 14) and (17, 6)? (a) (4, 4) (b) (10, 13) (c) (26, 20) (d) (13, 10)
  7. 7.What is the distance between the points (9, 15) and (15, 7)? (a) 14 (b) 100 (c) 11 (d) 10
  8. 8.What is the distance between the points (0, 3) and (4, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  9. 9.What is the distance between the points (1, 1) and (10, 13)? (a) 15 (b) 225 (c) 16 (d) 21
  10. 10.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  12. 12.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  14. 14.What is the distance between the points (4, 9) and (13, 21)? (a) 15 (b) 225 (c) 16 (d) 21
  15. 15.In which quadrant does the point (2, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (8, 14) and (18, 6)? (a) (13, 10) (b) (26, 20) (c) (10, 13) (d) (5, 4)
  17. 17.What is the distance between the points (9, 8) and (12, 4)? (a) 25 (b) 6 (c) 5 (d) 7
  18. 18.In which quadrant does the point (−6, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.What is the distance between the points (6, 10) and (21, 2)? (a) 289 (b) 23 (c) 17 (d) 18
  20. 20.What is the midpoint of the line joining (0, 8) and (12, 0)? (a) (7, 4) (b) (12, 8) (c) (4, 6) (d) (6, 4)
  21. 21.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  22. 22.What is the midpoint of the line joining (10, 13) and (22, 9)? (a) (16, 11) (b) (32, 22) (c) (6, 2) (d) (11, 16)
  23. 23.What is the distance between the points (4, 8) and (28, 15)? (a) 25 (b) 625 (c) 26 (d) 31
  24. 24.What is the midpoint of the line joining (7, 12) and (9, 8)? (a) (1, 2) (b) (16, 20) (c) (8, 10) (d) (10, 8)
  25. 25.What is the distance between the points (5, 8) and (13, 2)? (a) 11 (b) 100 (c) 14 (d) 10
  26. 26.What is the distance between the points (1, 7) and (10, 19)? (a) 21 (b) 15 (c) 225 (d) 16
  27. 27.What is the midpoint of the line joining (7, 1) and (9, 9)? (a) (1, 4) (b) (8, 5) (c) (5, 8) (d) (16, 10)
  28. 28.In which quadrant does the point (3, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.What is the distance between the points (1, 0) and (9, 6)? (a) 11 (b) 100 (c) 10 (d) 14
  30. 30.What is the midpoint of the line joining (4, 14) and (12, 10)? (a) (4, 2) (b) (16, 24) (c) (8, 12) (d) (12, 8)
  31. 31.In which quadrant does the point (−6, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  32. 32.What is the distance between the points (2, 2) and (5, 6)? (a) 7 (b) 5 (c) 25 (d) 6
  33. 33.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  34. 34.What is the distance between the points (6, 11) and (9, 7)? (a) 6 (b) 7 (c) 25 (d) 5
  35. 35.What is the distance between the points (6, 15) and (30, 8)? (a) 25 (b) 26 (c) 625 (d) 31
  36. 36.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  37. 37.What is the midpoint of the line joining (9, 8) and (15, 20)? (a) (12, 14) (b) (14, 12) (c) (24, 28) (d) (3, 6)
  38. 38.What is the distance between the points (7, 8) and (11, 11)? (a) 7 (b) 25 (c) 6 (d) 5
  39. 39.What is the midpoint of the line joining (0, 6) and (12, 2)? (a) (6, 4) (b) (12, 8) (c) (4, 6) (d) (6, 2)
  40. 40.In which quadrant does the point (−3, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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