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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 511 · 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.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  2. 2.What is the midpoint of the line joining (5, 12) and (17, 2)? (a) (6, 5) (b) (7, 11) (c) (22, 14) (d) (11, 7)
  3. 3.What is the midpoint of the line joining (3, 1) and (11, 13)? (a) (4, 6) (b) (7, 7) (c) (14, 14) (d) (8, 7)
  4. 4.What is the distance between the points (8, 11) and (23, 3)? (a) 23 (b) 17 (c) 289 (d) 18
  5. 5.In which quadrant does the point (3, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  6. 6.What is the distance between the points (0, 1) and (12, 6)? (a) 14 (b) 17 (c) 169 (d) 13
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  8. 8.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  9. 9.What is the midpoint of the line joining (5, 0) and (13, 8)? (a) (18, 8) (b) (4, 9) (c) (9, 4) (d) (4, 4)
  10. 10.What is the midpoint of the line joining (0, 4) and (4, 16)? (a) (2, 10) (b) (2, 6) (c) (4, 20) (d) (10, 2)
  11. 11.What is the distance between the points (5, 2) and (12, 26)? (a) 26 (b) 31 (c) 25 (d) 625
  12. 12.In which quadrant does the point (8, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  13. 13.In which quadrant does the point (−8, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (4, 21) and (9, 9)? (a) 169 (b) 17 (c) 14 (d) 13
  15. 15.What is the distance between the points (1, 13) and (9, 7)? (a) 100 (b) 10 (c) 11 (d) 14
  16. 16.What is the distance between the points (2, 2) and (14, 18)? (a) 28 (b) 400 (c) 21 (d) 20
  17. 17.What is the distance between the points (2, 9) and (8, 17)? (a) 10 (b) 14 (c) 11 (d) 100
  18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  20. 20.What is the midpoint of the line joining (2, 12) and (6, 10)? (a) (8, 22) (b) (11, 4) (c) (2, 1) (d) (4, 11)
  21. 21.In which quadrant does the point (−7, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.In which quadrant does the point (−9, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.In which quadrant does the point (−6, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (9, 9) and (12, 5)? (a) 25 (b) 5 (c) 6 (d) 7
  25. 25.What is the midpoint of the line joining (8, 12) and (16, 6)? (a) (9, 12) (b) (24, 18) (c) (12, 9) (d) (4, 3)
  26. 26.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the midpoint of the line joining (6, 12) and (14, 8)? (a) (20, 20) (b) (4, 2) (c) (10, 10) (d) (11, 10)
  28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  29. 29.What is the midpoint of the line joining (6, 3) and (10, 11)? (a) (8, 7) (b) (16, 14) (c) (7, 8) (d) (2, 4)
  30. 30.In which quadrant does the point (7, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.What is the distance between the points (1, 14) and (6, 2)? (a) 14 (b) 169 (c) 13 (d) 17
  32. 32.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  33. 33.What is the distance between the points (4, 3) and (20, 15)? (a) 21 (b) 400 (c) 28 (d) 20
  34. 34.In which quadrant does the point (−8, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (1, 13) and (5, 1)? (a) (3, 7) (b) (2, 6) (c) (7, 3) (d) (6, 14)
  36. 36.What is the midpoint of the line joining (9, 12) and (13, 0)? (a) (11, 6) (b) (6, 11) (c) (2, 6) (d) (22, 12)
  37. 37.What is the distance between the points (9, 4) and (12, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  38. 38.What is the distance between the points (0, 8) and (6, 16)? (a) 100 (b) 14 (c) 11 (d) 10
  39. 39.In which quadrant does the point (6, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  40. 40.What is the midpoint of the line joining (8, 7) and (16, 9)? (a) (24, 16) (b) (4, 1) (c) (8, 12) (d) (12, 8)

Answer key

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

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