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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 85 · 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 (2, 8) and (8, 12)? (a) (10, 20) (b) (10, 5) (c) (5, 10) (d) (3, 2)
  2. 2.What is the distance between the points (9, 8) and (12, 12)? (a) 25 (b) 7 (c) 6 (d) 5
  3. 3.What is the distance between the points (7, 3) and (10, 7)? (a) 25 (b) 5 (c) 7 (d) 6
  4. 4.In which quadrant does the point (9, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  5. 5.In which quadrant does the point (4, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  8. 8.What is the distance between the points (7, 13) and (22, 5)? (a) 18 (b) 23 (c) 289 (d) 17
  9. 9.In which quadrant does the point (2, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  10. 10.What is the midpoint of the line joining (0, 9) and (6, 13)? (a) (6, 22) (b) (3, 2) (c) (3, 11) (d) (11, 3)
  11. 11.What is the distance between the points (9, 24) and (17, 9)? (a) 17 (b) 289 (c) 23 (d) 18
  12. 12.What is the distance between the points (6, 9) and (18, 25)? (a) 28 (b) 400 (c) 20 (d) 21
  13. 13.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  14. 14.In which quadrant does the point (−8, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.In which quadrant does the point (2, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  16. 16.What is the distance between the points (9, 4) and (16, 28)? (a) 25 (b) 26 (c) 31 (d) 625
  17. 17.What is the midpoint of the line joining (9, 2) and (11, 4)? (a) (10, 3) (b) (3, 10) (c) (1, 1) (d) (20, 6)
  18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  19. 19.What is the midpoint of the line joining (6, 0) and (18, 2)? (a) (6, 1) (b) (1, 12) (c) (12, 1) (d) (24, 2)
  20. 20.What is the distance between the points (9, 20) and (21, 4)? (a) 400 (b) 21 (c) 28 (d) 20
  21. 21.What is the distance between the points (2, 11) and (5, 7)? (a) 7 (b) 25 (c) 5 (d) 6
  22. 22.What is the midpoint of the line joining (9, 10) and (17, 14)? (a) (4, 2) (b) (12, 13) (c) (26, 24) (d) (13, 12)
  23. 23.What is the distance between the points (1, 9) and (10, 21)? (a) 21 (b) 225 (c) 15 (d) 16
  24. 24.In which quadrant does the point (−9, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (4, 10) and (8, 8)? (a) (2, 1) (b) (6, 9) (c) (12, 18) (d) (9, 6)
  26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  27. 27.What is the midpoint of the line joining (9, 7) and (15, 5)? (a) (24, 12) (b) (12, 6) (c) (6, 12) (d) (3, 1)
  28. 28.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  29. 29.What is the midpoint of the line joining (8, 12) and (14, 8)? (a) (22, 20) (b) (11, 10) (c) (10, 11) (d) (3, 2)
  30. 30.What is the distance between the points (4, 5) and (8, 2)? (a) 5 (b) 25 (c) 6 (d) 7
  31. 31.In which quadrant does the point (2, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  32. 32.In which quadrant does the point (−8, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  33. 33.In which quadrant does the point (−3, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.What is the distance between the points (7, 21) and (23, 9)? (a) 400 (b) 28 (c) 21 (d) 20
  35. 35.What is the distance between the points (3, 18) and (8, 6)? (a) 169 (b) 14 (c) 13 (d) 17
  36. 36.In which quadrant does the point (−8, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  37. 37.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  39. 39.What is the distance between the points (9, 14) and (15, 6)? (a) 100 (b) 11 (c) 10 (d) 14
  40. 40.What is the distance between the points (1, 4) and (5, 7)? (a) 5 (b) 6 (c) 25 (d) 7

Answer key

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

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