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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 228 · 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 (9, 16) and (14, 4)? (a) 169 (b) 13 (c) 14 (d) 17
  2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  3. 3.What is the midpoint of the line joining (9, 11) and (17, 5)? (a) (4, 3) (b) (13, 8) (c) (8, 13) (d) (26, 16)
  4. 4.What is the distance between the points (9, 4) and (14, 16)? (a) 169 (b) 14 (c) 17 (d) 13
  5. 5.In which quadrant does the point (−4, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  7. 7.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  8. 8.What is the distance between the points (6, 1) and (30, 8)? (a) 25 (b) 26 (c) 625 (d) 31
  9. 9.What is the distance between the points (3, 5) and (12, 17)? (a) 16 (b) 15 (c) 21 (d) 225
  10. 10.What is the midpoint of the line joining (9, 11) and (21, 7)? (a) (9, 15) (b) (6, 2) (c) (30, 18) (d) (15, 9)
  11. 11.What is the distance between the points (7, 6) and (19, 22)? (a) 28 (b) 400 (c) 21 (d) 20
  12. 12.In which quadrant does the point (−5, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  14. 14.In which quadrant does the point (−4, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (3, 2) and (15, 14)? (a) (8, 9) (b) (6, 6) (c) (9, 8) (d) (18, 16)
  16. 16.What is the midpoint of the line joining (2, 14) and (12, 10)? (a) (7, 12) (b) (14, 24) (c) (5, 2) (d) (12, 7)
  17. 17.In which quadrant does the point (−8, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  18. 18.What is the distance between the points (0, 11) and (8, 5)? (a) 10 (b) 11 (c) 100 (d) 14
  19. 19.What is the distance between the points (7, 9) and (11, 12)? (a) 6 (b) 5 (c) 7 (d) 25
  20. 20.In which quadrant does the point (7, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  22. 22.In which quadrant does the point (5, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  23. 23.What is the distance between the points (2, 8) and (26, 1)? (a) 31 (b) 625 (c) 26 (d) 25
  24. 24.In which quadrant does the point (−6, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (2, 2) and (18, 14)? (a) 28 (b) 400 (c) 21 (d) 20
  26. 26.What is the distance between the points (6, 5) and (9, 9)? (a) 6 (b) 5 (c) 7 (d) 25
  27. 27.What is the distance between the points (7, 16) and (12, 4)? (a) 14 (b) 13 (c) 17 (d) 169
  28. 28.In which quadrant does the point (3, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  29. 29.What is the distance between the points (1, 9) and (5, 6)? (a) 7 (b) 6 (c) 5 (d) 25
  30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  31. 31.What is the distance between the points (0, 8) and (3, 12)? (a) 25 (b) 6 (c) 7 (d) 5
  32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  33. 33.In which quadrant does the point (7, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  34. 34.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  35. 35.What is the midpoint of the line joining (2, 10) and (4, 16)? (a) (13, 3) (b) (6, 26) (c) (1, 3) (d) (3, 13)
  36. 36.What is the distance between the points (0, 3) and (24, 10)? (a) 25 (b) 26 (c) 31 (d) 625
  37. 37.What is the distance between the points (3, 0) and (9, 8)? (a) 14 (b) 10 (c) 100 (d) 11
  38. 38.What is the distance between the points (2, 8) and (6, 11)? (a) 25 (b) 6 (c) 5 (d) 7
  39. 39.In which quadrant does the point (3, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  40. 40.In which quadrant does the point (6, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant

Answer key

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

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