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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 182 · 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.In which quadrant does the point (7, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  5. 5.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the distance between the points (2, 4) and (5, 8)? (a) 7 (b) 5 (c) 25 (d) 6
  7. 7.What is the distance between the points (2, 11) and (8, 3)? (a) 11 (b) 14 (c) 100 (d) 10
  8. 8.What is the distance between the points (1, 6) and (8, 30)? (a) 25 (b) 31 (c) 625 (d) 26
  9. 9.What is the midpoint of the line joining (8, 10) and (10, 12)? (a) (18, 22) (b) (1, 1) (c) (9, 11) (d) (11, 9)
  10. 10.In which quadrant does the point (3, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  12. 12.What is the distance between the points (1, 2) and (7, 10)? (a) 100 (b) 14 (c) 10 (d) 11
  13. 13.What is the distance between the points (2, 1) and (14, 10)? (a) 16 (b) 21 (c) 15 (d) 225
  14. 14.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  16. 16.What is the distance between the points (0, 33) and (7, 9)? (a) 31 (b) 25 (c) 26 (d) 625
  17. 17.What is the midpoint of the line joining (7, 7) and (13, 15)? (a) (11, 10) (b) (3, 4) (c) (20, 22) (d) (10, 11)
  18. 18.What is the distance between the points (2, 2) and (5, 6)? (a) 25 (b) 7 (c) 6 (d) 5
  19. 19.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (4, 3) and (6, 5)? (a) (4, 5) (b) (10, 8) (c) (1, 1) (d) (5, 4)
  21. 21.What is the midpoint of the line joining (9, 12) and (15, 10)? (a) (11, 12) (b) (3, 1) (c) (24, 22) (d) (12, 11)
  22. 22.In which quadrant does the point (9, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  24. 24.What is the distance between the points (2, 33) and (9, 9)? (a) 26 (b) 31 (c) 625 (d) 25
  25. 25.In which quadrant does the point (−3, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  26. 26.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  27. 27.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  29. 29.What is the midpoint of the line joining (4, 12) and (10, 8)? (a) (7, 10) (b) (3, 2) (c) (10, 7) (d) (14, 20)
  30. 30.What is the midpoint of the line joining (7, 7) and (19, 3)? (a) (13, 5) (b) (5, 13) (c) (26, 10) (d) (6, 2)
  31. 31.What is the midpoint of the line joining (1, 12) and (13, 2)? (a) (6, 5) (b) (7, 7) (c) (8, 7) (d) (14, 14)
  32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  33. 33.In which quadrant does the point (8, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  34. 34.What is the midpoint of the line joining (0, 0) and (4, 4)? (a) (3, 2) (b) (2, 2) (c) (4, 4) (d) (2, 3)
  35. 35.In which quadrant does the point (6, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the distance between the points (3, 0) and (12, 12)? (a) 15 (b) 21 (c) 16 (d) 225
  37. 37.In which quadrant does the point (6, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the distance between the points (8, 1) and (11, 5)? (a) 25 (b) 6 (c) 5 (d) 7
  39. 39.What is the distance between the points (7, 4) and (23, 16)? (a) 28 (b) 20 (c) 21 (d) 400
  40. 40.In which quadrant does the point (−8, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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