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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 861 · 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 (5, 13) and (10, 1)? (a) 14 (b) 169 (c) 17 (d) 13
  2. 2.What is the midpoint of the line joining (6, 12) and (10, 10)? (a) (8, 11) (b) (16, 22) (c) (11, 8) (d) (2, 1)
  3. 3.What is the midpoint of the line joining (8, 9) and (12, 11)? (a) (2, 1) (b) (11, 10) (c) (20, 20) (d) (10, 10)
  4. 4.What is the distance between the points (6, 10) and (21, 2)? (a) 289 (b) 18 (c) 23 (d) 17
  5. 5.What is the distance between the points (1, 13) and (6, 1)? (a) 169 (b) 13 (c) 17 (d) 14
  6. 6.In which quadrant does the point (7, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  8. 8.In which quadrant does the point (−6, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  9. 9.What is the distance between the points (8, 19) and (20, 3)? (a) 21 (b) 20 (c) 400 (d) 28
  10. 10.In which quadrant does the point (7, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  11. 11.In which quadrant does the point (−8, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.In which quadrant does the point (−3, 9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.In which quadrant does the point (−7, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.What is the distance between the points (4, 6) and (20, 18)? (a) 400 (b) 20 (c) 28 (d) 21
  15. 15.What is the distance between the points (2, 9) and (10, 3)? (a) 14 (b) 100 (c) 10 (d) 11
  16. 16.What is the distance between the points (3, 29) and (10, 5)? (a) 26 (b) 625 (c) 25 (d) 31
  17. 17.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  18. 18.In which quadrant does the point (9, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.What is the midpoint of the line joining (3, 20) and (15, 8)? (a) (14, 9) (b) (9, 14) (c) (18, 28) (d) (6, 6)
  20. 20.What is the midpoint of the line joining (7, 15) and (17, 9)? (a) (5, 3) (b) (12, 12) (c) (13, 12) (d) (24, 24)
  21. 21.What is the midpoint of the line joining (2, 7) and (4, 5)? (a) (6, 3) (b) (1, 1) (c) (6, 12) (d) (3, 6)
  22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  23. 23.What is the midpoint of the line joining (5, 8) and (11, 16)? (a) (12, 8) (b) (3, 4) (c) (16, 24) (d) (8, 12)
  24. 24.In which quadrant does the point (7, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  25. 25.What is the distance between the points (9, 20) and (17, 5)? (a) 17 (b) 18 (c) 289 (d) 23
  26. 26.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  28. 28.What is the midpoint of the line joining (6, 10) and (10, 18)? (a) (14, 8) (b) (16, 28) (c) (8, 14) (d) (2, 4)
  29. 29.What is the distance between the points (8, 7) and (23, 15)? (a) 18 (b) 17 (c) 289 (d) 23
  30. 30.In which quadrant does the point (5, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  32. 32.What is the midpoint of the line joining (8, 4) and (16, 0)? (a) (24, 4) (b) (2, 12) (c) (4, 2) (d) (12, 2)
  33. 33.In which quadrant does the point (−8, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (1, 8) and (6, 20)? (a) 14 (b) 169 (c) 13 (d) 17
  35. 35.What is the distance between the points (4, 2) and (19, 10)? (a) 18 (b) 23 (c) 289 (d) 17
  36. 36.What is the midpoint of the line joining (8, 20) and (18, 8)? (a) (14, 13) (b) (26, 28) (c) (13, 14) (d) (5, 6)
  37. 37.What is the distance between the points (1, 4) and (10, 16)? (a) 21 (b) 16 (c) 15 (d) 225
  38. 38.What is the midpoint of the line joining (0, 5) and (6, 17)? (a) (3, 11) (b) (6, 22) (c) (3, 6) (d) (11, 3)
  39. 39.In which quadrant does the point (8, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (6, 7) and (14, 1)? (a) 10 (b) 11 (c) 14 (d) 100

Answer key

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

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