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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 211 · 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, 1) and (6, 13)? (a) 17 (b) 169 (c) 13 (d) 14
  2. 2.What is the midpoint of the line joining (3, 5) and (9, 17)? (a) (12, 22) (b) (6, 11) (c) (3, 6) (d) (11, 6)
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  4. 4.What is the distance between the points (0, 12) and (3, 8)? (a) 6 (b) 5 (c) 7 (d) 25
  5. 5.What is the midpoint of the line joining (4, 9) and (8, 7)? (a) (12, 16) (b) (2, 1) (c) (6, 8) (d) (8, 6)
  6. 6.What is the distance between the points (4, 3) and (19, 11)? (a) 23 (b) 17 (c) 289 (d) 18
  7. 7.What is the midpoint of the line joining (6, 0) and (18, 12)? (a) (12, 6) (b) (24, 12) (c) (6, 6) (d) (6, 12)
  8. 8.In which quadrant does the point (8, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  9. 9.In which quadrant does the point (6, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  11. 11.What is the distance between the points (1, 12) and (16, 4)? (a) 23 (b) 17 (c) 289 (d) 18
  12. 12.What is the distance between the points (0, 9) and (3, 13)? (a) 25 (b) 6 (c) 7 (d) 5
  13. 13.What is the distance between the points (9, 0) and (14, 12)? (a) 169 (b) 13 (c) 14 (d) 17
  14. 14.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.What is the midpoint of the line joining (3, 8) and (5, 4)? (a) (6, 4) (b) (4, 6) (c) (8, 12) (d) (1, 2)
  16. 16.In which quadrant does the point (1, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the midpoint of the line joining (5, 20) and (7, 8)? (a) (6, 14) (b) (1, 6) (c) (12, 28) (d) (14, 6)
  18. 18.In which quadrant does the point (6, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  19. 19.In which quadrant does the point (6, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  21. 21.In which quadrant does the point (3, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  23. 23.What is the midpoint of the line joining (0, 7) and (2, 13)? (a) (10, 1) (b) (2, 20) (c) (1, 10) (d) (1, 3)
  24. 24.In which quadrant does the point (3, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.What is the midpoint of the line joining (8, 13) and (16, 3)? (a) (4, 5) (b) (24, 16) (c) (12, 8) (d) (8, 12)
  26. 26.What is the distance between the points (1, 15) and (9, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  27. 27.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (1, 19) and (7, 9)? (a) (4, 14) (b) (8, 28) (c) (3, 5) (d) (14, 4)
  29. 29.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  30. 30.What is the midpoint of the line joining (9, 7) and (17, 11)? (a) (4, 2) (b) (9, 13) (c) (13, 9) (d) (26, 18)
  31. 31.In which quadrant does the point (9, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the distance between the points (7, 27) and (14, 3)? (a) 26 (b) 25 (c) 31 (d) 625
  33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  34. 34.What is the midpoint of the line joining (7, 10) and (13, 22)? (a) (3, 6) (b) (20, 32) (c) (10, 16) (d) (16, 10)
  35. 35.What is the distance between the points (8, 14) and (17, 2)? (a) 225 (b) 21 (c) 16 (d) 15
  36. 36.What is the distance between the points (4, 7) and (8, 10)? (a) 6 (b) 25 (c) 5 (d) 7
  37. 37.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  38. 38.What is the distance between the points (1, 8) and (16, 16)? (a) 23 (b) 18 (c) 17 (d) 289
  39. 39.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26

Answer key

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

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