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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 886 · 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 (5, 10) and (11, 2)? (a) (6, 8) (b) (16, 12) (c) (8, 6) (d) (3, 4)
  2. 2.What is the midpoint of the line joining (0, 9) and (6, 5)? (a) (3, 7) (b) (6, 14) (c) (7, 3) (d) (3, 2)
  3. 3.In which quadrant does the point (−9, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  5. 5.What is the distance between the points (6, 2) and (13, 26)? (a) 625 (b) 26 (c) 31 (d) 25
  6. 6.What is the midpoint of the line joining (5, 7) and (13, 1)? (a) (4, 9) (b) (4, 3) (c) (9, 4) (d) (18, 8)
  7. 7.In which quadrant does the point (6, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (4, 11) and (10, 9)? (a) (14, 20) (b) (3, 1) (c) (7, 10) (d) (10, 7)
  9. 9.What is the distance between the points (4, 21) and (13, 9)? (a) 225 (b) 15 (c) 16 (d) 21
  10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  11. 11.In which quadrant does the point (−7, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  13. 13.In which quadrant does the point (2, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.What is the distance between the points (2, 15) and (11, 3)? (a) 225 (b) 21 (c) 16 (d) 15
  15. 15.What is the midpoint of the line joining (0, 6) and (4, 10)? (a) (8, 2) (b) (2, 2) (c) (2, 8) (d) (4, 16)
  16. 16.What is the distance between the points (2, 0) and (5, 4)? (a) 6 (b) 5 (c) 7 (d) 25
  17. 17.What is the midpoint of the line joining (7, 5) and (11, 13)? (a) (2, 4) (b) (9, 9) (c) (18, 18) (d) (10, 9)
  18. 18.What is the midpoint of the line joining (4, 20) and (14, 10)? (a) (15, 9) (b) (18, 30) (c) (9, 15) (d) (5, 5)
  19. 19.In which quadrant does the point (5, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the midpoint of the line joining (1, 2) and (11, 14)? (a) (6, 8) (b) (12, 16) (c) (8, 6) (d) (5, 6)
  21. 21.What is the distance between the points (9, 2) and (24, 10)? (a) 289 (b) 18 (c) 17 (d) 23
  22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  23. 23.What is the distance between the points (5, 2) and (21, 14)? (a) 28 (b) 400 (c) 21 (d) 20
  24. 24.In which quadrant does the point (−4, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  26. 26.What is the midpoint of the line joining (0, 4) and (2, 10)? (a) (1, 3) (b) (7, 1) (c) (1, 7) (d) (2, 14)
  27. 27.In which quadrant does the point (−8, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  29. 29.What is the distance between the points (9, 19) and (21, 3)? (a) 400 (b) 21 (c) 28 (d) 20
  30. 30.What is the midpoint of the line joining (0, 15) and (6, 3)? (a) (3, 6) (b) (3, 9) (c) (6, 18) (d) (9, 3)
  31. 31.What is the midpoint of the line joining (2, 3) and (8, 1)? (a) (2, 5) (b) (10, 4) (c) (3, 1) (d) (5, 2)
  32. 32.In which quadrant does the point (5, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  33. 33.What is the midpoint of the line joining (0, 2) and (12, 4)? (a) (12, 6) (b) (6, 1) (c) (3, 6) (d) (6, 3)
  34. 34.What is the midpoint of the line joining (9, 14) and (13, 10)? (a) (22, 24) (b) (12, 11) (c) (2, 2) (d) (11, 12)
  35. 35.What is the midpoint of the line joining (6, 6) and (12, 8)? (a) (3, 1) (b) (7, 9) (c) (18, 14) (d) (9, 7)
  36. 36.What is the distance between the points (6, 3) and (18, 12)? (a) 225 (b) 16 (c) 21 (d) 15
  37. 37.In which quadrant does the point (−1, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  38. 38.What is the distance between the points (8, 4) and (23, 12)? (a) 18 (b) 289 (c) 17 (d) 23
  39. 39.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5

Answer key

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

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