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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 125 · 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 (10, 9) and (22, 17)? (a) (6, 4) (b) (16, 13) (c) (32, 26) (d) (13, 16)
  2. 2.What is the distance between the points (7, 6) and (16, 18)? (a) 21 (b) 225 (c) 16 (d) 15
  3. 3.In which quadrant does the point (3, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the distance between the points (6, 4) and (9, 8)? (a) 5 (b) 25 (c) 6 (d) 7
  5. 5.What is the midpoint of the line joining (6, 7) and (18, 1)? (a) (24, 8) (b) (12, 4) (c) (4, 12) (d) (6, 3)
  6. 6.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  7. 7.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (1, 14) and (11, 6)? (a) (10, 6) (b) (12, 20) (c) (5, 4) (d) (6, 10)
  9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  10. 10.What is the midpoint of the line joining (2, 15) and (12, 5)? (a) (7, 10) (b) (5, 5) (c) (14, 20) (d) (10, 7)
  11. 11.In which quadrant does the point (4, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  12. 12.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  13. 13.What is the distance between the points (1, 9) and (9, 3)? (a) 10 (b) 14 (c) 11 (d) 100
  14. 14.What is the distance between the points (8, 16) and (32, 9)? (a) 625 (b) 25 (c) 26 (d) 31
  15. 15.What is the distance between the points (7, 14) and (12, 2)? (a) 14 (b) 169 (c) 17 (d) 13
  16. 16.What is the distance between the points (8, 9) and (11, 13)? (a) 7 (b) 25 (c) 5 (d) 6
  17. 17.What is the distance between the points (6, 16) and (22, 4)? (a) 28 (b) 21 (c) 400 (d) 20
  18. 18.What is the midpoint of the line joining (8, 10) and (14, 6)? (a) (22, 16) (b) (8, 11) (c) (3, 2) (d) (11, 8)
  19. 19.What is the distance between the points (8, 17) and (16, 2)? (a) 289 (b) 18 (c) 17 (d) 23
  20. 20.What is the distance between the points (2, 6) and (5, 2)? (a) 25 (b) 6 (c) 7 (d) 5
  21. 21.In which quadrant does the point (3, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.What is the distance between the points (6, 9) and (30, 16)? (a) 26 (b) 25 (c) 31 (d) 625
  23. 23.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  25. 25.In which quadrant does the point (6, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  27. 27.What is the distance between the points (5, 11) and (20, 3)? (a) 18 (b) 17 (c) 289 (d) 23
  28. 28.What is the midpoint of the line joining (9, 5) and (13, 9)? (a) (7, 11) (b) (2, 2) (c) (22, 14) (d) (11, 7)
  29. 29.What is the midpoint of the line joining (4, 0) and (16, 4)? (a) (20, 4) (b) (10, 2) (c) (2, 10) (d) (6, 2)
  30. 30.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  31. 31.In which quadrant does the point (9, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  32. 32.What is the distance between the points (5, 23) and (13, 8)? (a) 23 (b) 289 (c) 17 (d) 18
  33. 33.In which quadrant does the point (−9, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  34. 34.What is the distance between the points (0, 7) and (12, 23)? (a) 400 (b) 21 (c) 28 (d) 20
  35. 35.What is the midpoint of the line joining (6, 8) and (8, 10)? (a) (1, 1) (b) (14, 18) (c) (7, 9) (d) (9, 7)
  36. 36.What is the distance between the points (6, 12) and (12, 4)? (a) 10 (b) 100 (c) 11 (d) 14
  37. 37.In which quadrant does the point (−2, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the distance between the points (3, 1) and (10, 25)? (a) 31 (b) 26 (c) 25 (d) 625
  39. 39.What is the midpoint of the line joining (3, 13) and (7, 9)? (a) (5, 11) (b) (2, 2) (c) (10, 22) (d) (11, 5)
  40. 40.What is the midpoint of the line joining (4, 1) and (16, 7)? (a) (6, 3) (b) (20, 8) (c) (10, 4) (d) (4, 10)

Answer key

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

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