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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 539 · 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 (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  2. 2.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  3. 3.What is the midpoint of the line joining (10, 12) and (12, 10)? (a) (22, 22) (b) (12, 11) (c) (1, 1) (d) (11, 11)
  4. 4.What is the distance between the points (0, 11) and (3, 7)? (a) 6 (b) 5 (c) 25 (d) 7
  5. 5.What is the midpoint of the line joining (4, 4) and (6, 14)? (a) (10, 18) (b) (5, 9) (c) (9, 5) (d) (1, 5)
  6. 6.What is the distance between the points (6, 15) and (21, 7)? (a) 17 (b) 23 (c) 18 (d) 289
  7. 7.What is the midpoint of the line joining (0, 2) and (8, 0)? (a) (4, 1) (b) (8, 2) (c) (5, 1) (d) (1, 4)
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  9. 9.What is the distance between the points (2, 13) and (11, 1)? (a) 21 (b) 16 (c) 15 (d) 225
  10. 10.What is the midpoint of the line joining (9, 12) and (15, 6)? (a) (9, 12) (b) (24, 18) (c) (3, 3) (d) (12, 9)
  11. 11.What is the midpoint of the line joining (3, 7) and (7, 17)? (a) (12, 5) (b) (2, 5) (c) (10, 24) (d) (5, 12)
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  13. 13.In which quadrant does the point (−9, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  14. 14.What is the distance between the points (1, 14) and (9, 8)? (a) 11 (b) 10 (c) 14 (d) 100
  15. 15.In which quadrant does the point (−8, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  17. 17.What is the midpoint of the line joining (4, 14) and (14, 8)? (a) (11, 9) (b) (18, 22) (c) (5, 3) (d) (9, 11)
  18. 18.In which quadrant does the point (−2, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.What is the distance between the points (3, 12) and (19, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  20. 20.What is the distance between the points (4, 5) and (8, 8)? (a) 7 (b) 5 (c) 6 (d) 25
  21. 21.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.What is the distance between the points (0, 1) and (16, 13)? (a) 400 (b) 28 (c) 21 (d) 20
  23. 23.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.What is the midpoint of the line joining (6, 15) and (18, 7)? (a) (24, 22) (b) (11, 12) (c) (12, 11) (d) (6, 4)
  25. 25.What is the midpoint of the line joining (5, 16) and (13, 10)? (a) (4, 3) (b) (13, 9) (c) (18, 26) (d) (9, 13)
  26. 26.What is the distance between the points (5, 6) and (11, 14)? (a) 100 (b) 10 (c) 11 (d) 14
  27. 27.In which quadrant does the point (−4, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  28. 28.What is the distance between the points (5, 9) and (12, 33)? (a) 26 (b) 25 (c) 625 (d) 31
  29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  30. 30.In which quadrant does the point (8, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (3, 6) and (5, 4)? (a) (5, 4) (b) (4, 5) (c) (1, 1) (d) (8, 10)
  32. 32.In which quadrant does the point (5, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  33. 33.What is the distance between the points (6, 5) and (22, 17)? (a) 28 (b) 400 (c) 20 (d) 21
  34. 34.What is the distance between the points (4, 9) and (10, 1)? (a) 100 (b) 11 (c) 14 (d) 10
  35. 35.What is the midpoint of the line joining (1, 8) and (3, 20)? (a) (14, 2) (b) (1, 6) (c) (2, 14) (d) (4, 28)
  36. 36.In which quadrant does the point (−7, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (1, 4) and (5, 8)? (a) (3, 6) (b) (2, 2) (c) (6, 12) (d) (6, 3)
  38. 38.What is the distance between the points (7, 12) and (13, 4)? (a) 11 (b) 10 (c) 100 (d) 14
  39. 39.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  40. 40.What is the midpoint of the line joining (3, 4) and (7, 12)? (a) (2, 4) (b) (10, 16) (c) (5, 8) (d) (8, 5)

Answer key

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

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