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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 330 · 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 midpoint of the line joining (6, 20) and (8, 8)? (a) (14, 28) (b) (1, 6) (c) (14, 7) (d) (7, 14)
  2. 2.What is the distance between the points (3, 5) and (7, 8)? (a) 5 (b) 7 (c) 25 (d) 6
  3. 3.What is the midpoint of the line joining (10, 13) and (18, 5)? (a) (4, 4) (b) (14, 9) (c) (28, 18) (d) (9, 14)
  4. 4.In which quadrant does the point (9, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  6. 6.In which quadrant does the point (1, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.What is the distance between the points (2, 7) and (5, 11)? (a) 7 (b) 6 (c) 5 (d) 25
  8. 8.What is the distance between the points (7, 11) and (10, 7)? (a) 7 (b) 25 (c) 6 (d) 5
  9. 9.What is the midpoint of the line joining (4, 16) and (14, 8)? (a) (12, 9) (b) (9, 12) (c) (5, 4) (d) (18, 24)
  10. 10.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  12. 12.What is the distance between the points (0, 8) and (3, 12)? (a) 7 (b) 25 (c) 5 (d) 6
  13. 13.In which quadrant does the point (2, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (0, 8) and (10, 12)? (a) (10, 5) (b) (5, 2) (c) (10, 20) (d) (5, 10)
  15. 15.What is the midpoint of the line joining (9, 4) and (15, 10)? (a) (3, 3) (b) (12, 7) (c) (24, 14) (d) (7, 12)
  16. 16.In which quadrant does the point (7, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  17. 17.In which quadrant does the point (−2, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  18. 18.What is the midpoint of the line joining (9, 7) and (11, 5)? (a) (20, 12) (b) (1, 1) (c) (6, 10) (d) (10, 6)
  19. 19.What is the midpoint of the line joining (3, 14) and (15, 8)? (a) (18, 22) (b) (9, 11) (c) (11, 9) (d) (6, 3)
  20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  23. 23.What is the midpoint of the line joining (9, 2) and (17, 14)? (a) (8, 13) (b) (4, 6) (c) (26, 16) (d) (13, 8)
  24. 24.What is the distance between the points (0, 3) and (24, 10)? (a) 25 (b) 31 (c) 625 (d) 26
  25. 25.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  26. 26.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  27. 27.What is the distance between the points (0, 4) and (3, 8)? (a) 6 (b) 5 (c) 7 (d) 25
  28. 28.What is the distance between the points (1, 15) and (16, 7)? (a) 18 (b) 289 (c) 17 (d) 23
  29. 29.What is the midpoint of the line joining (7, 4) and (9, 0)? (a) (1, 2) (b) (16, 4) (c) (8, 2) (d) (2, 8)
  30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  31. 31.In which quadrant does the point (−9, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.In which quadrant does the point (2, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.In which quadrant does the point (−3, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (1, 2) and (9, 12)? (a) (5, 7) (b) (10, 14) (c) (7, 5) (d) (4, 5)
  35. 35.What is the midpoint of the line joining (3, 10) and (13, 22)? (a) (16, 32) (b) (8, 16) (c) (5, 6) (d) (16, 8)
  36. 36.What is the distance between the points (1, 3) and (6, 15)? (a) 13 (b) 17 (c) 14 (d) 169
  37. 37.What is the distance between the points (2, 19) and (11, 7)? (a) 225 (b) 21 (c) 15 (d) 16
  38. 38.What is the distance between the points (8, 8) and (11, 12)? (a) 6 (b) 25 (c) 5 (d) 7
  39. 39.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  40. 40.What is the midpoint of the line joining (2, 14) and (6, 2)? (a) (4, 8) (b) (2, 6) (c) (8, 16) (d) (8, 4)

Answer key

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

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