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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 475 · 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 (8, 9) and (18, 11)? (a) (10, 13) (b) (26, 20) (c) (5, 1) (d) (13, 10)
  2. 2.What is the midpoint of the line joining (10, 13) and (14, 7)? (a) (24, 20) (b) (12, 10) (c) (10, 12) (d) (2, 3)
  3. 3.In which quadrant does the point (8, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the midpoint of the line joining (0, 2) and (8, 4)? (a) (8, 6) (b) (4, 3) (c) (3, 4) (d) (4, 1)
  5. 5.In which quadrant does the point (8, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.In which quadrant does the point (−4, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  8. 8.What is the distance between the points (6, 13) and (18, 8)? (a) 17 (b) 169 (c) 13 (d) 14
  9. 9.What is the midpoint of the line joining (6, 16) and (12, 8)? (a) (18, 24) (b) (9, 12) (c) (12, 9) (d) (3, 4)
  10. 10.What is the distance between the points (0, 19) and (5, 7)? (a) 14 (b) 169 (c) 17 (d) 13
  11. 11.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  12. 12.What is the distance between the points (0, 9) and (6, 1)? (a) 14 (b) 11 (c) 10 (d) 100
  13. 13.What is the midpoint of the line joining (4, 0) and (8, 8)? (a) (4, 6) (b) (6, 4) (c) (12, 8) (d) (2, 4)
  14. 14.What is the midpoint of the line joining (10, 1) and (18, 5)? (a) (4, 2) (b) (28, 6) (c) (3, 14) (d) (14, 3)
  15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  17. 17.What is the midpoint of the line joining (5, 2) and (17, 0)? (a) (11, 1) (b) (1, 11) (c) (22, 2) (d) (6, 1)
  18. 18.What is the distance between the points (4, 4) and (19, 12)? (a) 18 (b) 17 (c) 289 (d) 23
  19. 19.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.What is the midpoint of the line joining (9, 9) and (15, 13)? (a) (11, 12) (b) (3, 2) (c) (12, 11) (d) (24, 22)
  21. 21.What is the midpoint of the line joining (9, 22) and (15, 10)? (a) (3, 6) (b) (16, 12) (c) (12, 16) (d) (24, 32)
  22. 22.What is the midpoint of the line joining (7, 19) and (13, 7)? (a) (3, 6) (b) (13, 10) (c) (10, 13) (d) (20, 26)
  23. 23.What is the midpoint of the line joining (5, 9) and (17, 7)? (a) (8, 11) (b) (22, 16) (c) (6, 1) (d) (11, 8)
  24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  26. 26.What is the distance between the points (0, 4) and (8, 19)? (a) 23 (b) 289 (c) 17 (d) 18
  27. 27.What is the midpoint of the line joining (8, 8) and (10, 2)? (a) (9, 5) (b) (18, 10) (c) (1, 3) (d) (5, 9)
  28. 28.What is the midpoint of the line joining (3, 12) and (15, 8)? (a) (6, 2) (b) (18, 20) (c) (10, 9) (d) (9, 10)
  29. 29.What is the distance between the points (1, 6) and (10, 18)? (a) 21 (b) 15 (c) 225 (d) 16
  30. 30.What is the midpoint of the line joining (10, 0) and (14, 8)? (a) (24, 8) (b) (4, 12) (c) (12, 4) (d) (2, 4)
  31. 31.What is the midpoint of the line joining (4, 10) and (6, 14)? (a) (1, 2) (b) (5, 12) (c) (10, 24) (d) (12, 5)
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  33. 33.What is the distance between the points (9, 6) and (21, 15)? (a) 225 (b) 15 (c) 21 (d) 16
  34. 34.What is the distance between the points (7, 16) and (12, 4)? (a) 169 (b) 14 (c) 17 (d) 13
  35. 35.In which quadrant does the point (−8, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  36. 36.What is the distance between the points (7, 8) and (15, 14)? (a) 11 (b) 10 (c) 100 (d) 14
  37. 37.What is the midpoint of the line joining (3, 0) and (15, 4)? (a) (2, 9) (b) (18, 4) (c) (9, 2) (d) (6, 2)
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  40. 40.In which quadrant does the point (−1, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant

Answer key

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

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