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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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