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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 901 · 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 (4, 1) and (12, 16)? (a) 17 (b) 18 (c) 289 (d) 23
  2. 2.What is the distance between the points (5, 4) and (9, 1)? (a) 6 (b) 7 (c) 5 (d) 25
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  4. 4.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  7. 7.In which quadrant does the point (−8, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  8. 8.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  13. 13.What is the midpoint of the line joining (3, 8) and (9, 16)? (a) (12, 6) (b) (6, 12) (c) (12, 24) (d) (3, 4)
  14. 14.What is the midpoint of the line joining (5, 21) and (13, 9)? (a) (18, 30) (b) (4, 6) (c) (9, 15) (d) (15, 9)
  15. 15.What is the distance between the points (1, 12) and (16, 4)? (a) 18 (b) 17 (c) 289 (d) 23
  16. 16.In which quadrant does the point (8, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  17. 17.In which quadrant does the point (6, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  18. 18.In which quadrant does the point (−9, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (7, 14) and (31, 7)? (a) 625 (b) 31 (c) 25 (d) 26
  20. 20.What is the distance between the points (8, 5) and (11, 9)? (a) 5 (b) 6 (c) 25 (d) 7
  21. 21.What is the distance between the points (3, 7) and (11, 13)? (a) 14 (b) 100 (c) 11 (d) 10
  22. 22.What is the distance between the points (9, 10) and (21, 1)? (a) 225 (b) 21 (c) 16 (d) 15
  23. 23.What is the distance between the points (9, 8) and (24, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  24. 24.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  25. 25.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (6, 9) and (18, 18)? (a) 21 (b) 16 (c) 225 (d) 15
  27. 27.What is the distance between the points (7, 4) and (11, 7)? (a) 6 (b) 7 (c) 5 (d) 25
  28. 28.In which quadrant does the point (−8, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.In which quadrant does the point (6, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  30. 30.In which quadrant does the point (8, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  31. 31.What is the distance between the points (0, 8) and (8, 2)? (a) 100 (b) 11 (c) 10 (d) 14
  32. 32.What is the midpoint of the line joining (2, 4) and (12, 14)? (a) (14, 18) (b) (5, 5) (c) (7, 9) (d) (9, 7)
  33. 33.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  34. 34.What is the distance between the points (4, 13) and (10, 5)? (a) 14 (b) 11 (c) 100 (d) 10
  35. 35.What is the distance between the points (4, 3) and (12, 18)? (a) 17 (b) 18 (c) 289 (d) 23
  36. 36.What is the distance between the points (4, 0) and (13, 12)? (a) 21 (b) 225 (c) 15 (d) 16
  37. 37.In which quadrant does the point (6, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.What is the distance between the points (5, 8) and (8, 12)? (a) 5 (b) 6 (c) 7 (d) 25
  39. 39.In which quadrant does the point (4, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.What is the midpoint of the line joining (7, 9) and (15, 11)? (a) (11, 10) (b) (4, 1) (c) (22, 20) (d) (10, 11)

Answer key

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

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