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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 142 · 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 (−8, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  4. 4.What is the midpoint of the line joining (3, 7) and (13, 3)? (a) (5, 8) (b) (5, 2) (c) (16, 10) (d) (8, 5)
  5. 5.What is the midpoint of the line joining (2, 7) and (12, 13)? (a) (14, 20) (b) (5, 3) (c) (7, 10) (d) (10, 7)
  6. 6.What is the distance between the points (5, 4) and (20, 12)? (a) 18 (b) 17 (c) 23 (d) 289
  7. 7.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  9. 9.What is the midpoint of the line joining (8, 5) and (12, 3)? (a) (4, 10) (b) (2, 1) (c) (10, 4) (d) (20, 8)
  10. 10.What is the distance between the points (8, 9) and (20, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  15. 15.What is the distance between the points (5, 20) and (14, 8)? (a) 21 (b) 225 (c) 15 (d) 16
  16. 16.In which quadrant does the point (4, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  17. 17.What is the distance between the points (1, 7) and (25, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  18. 18.What is the midpoint of the line joining (6, 2) and (18, 0)? (a) (12, 1) (b) (1, 12) (c) (6, 1) (d) (24, 2)
  19. 19.What is the distance between the points (9, 13) and (18, 1)? (a) 15 (b) 16 (c) 225 (d) 21
  20. 20.In which quadrant does the point (−8, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  22. 22.What is the distance between the points (9, 13) and (17, 7)? (a) 14 (b) 100 (c) 10 (d) 11
  23. 23.What is the midpoint of the line joining (10, 4) and (18, 12)? (a) (4, 4) (b) (28, 16) (c) (14, 8) (d) (8, 14)
  24. 24.What is the midpoint of the line joining (10, 12) and (12, 4)? (a) (22, 16) (b) (8, 11) (c) (1, 4) (d) (11, 8)
  25. 25.What is the midpoint of the line joining (9, 1) and (13, 13)? (a) (22, 14) (b) (2, 6) (c) (7, 11) (d) (11, 7)
  26. 26.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  27. 27.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  28. 28.What is the distance between the points (0, 14) and (16, 2)? (a) 20 (b) 400 (c) 28 (d) 21
  29. 29.In which quadrant does the point (−4, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  30. 30.What is the midpoint of the line joining (0, 2) and (2, 10)? (a) (2, 12) (b) (1, 6) (c) (6, 1) (d) (1, 4)
  31. 31.What is the midpoint of the line joining (2, 8) and (4, 10)? (a) (6, 18) (b) (3, 9) (c) (9, 3) (d) (1, 1)
  32. 32.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  33. 33.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  34. 34.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (−7, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  36. 36.What is the midpoint of the line joining (4, 4) and (10, 10)? (a) (3, 3) (b) (7, 7) (c) (14, 14) (d) (8, 7)
  37. 37.What is the midpoint of the line joining (9, 10) and (13, 2)? (a) (6, 11) (b) (11, 6) (c) (2, 4) (d) (22, 12)
  38. 38.What is the distance between the points (1, 8) and (25, 1)? (a) 625 (b) 25 (c) 26 (d) 31
  39. 39.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the distance between the points (1, 6) and (5, 9)? (a) 5 (b) 6 (c) 25 (d) 7

Answer key

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

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