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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 521 · 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 (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  2. 2.What is the midpoint of the line joining (0, 0) and (12, 12)? (a) (12, 12) (b) (7, 6) (c) (6, 7) (d) (6, 6)
  3. 3.What is the distance between the points (1, 3) and (6, 15)? (a) 169 (b) 14 (c) 13 (d) 17
  4. 4.In which quadrant does the point (−8, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  6. 6.In which quadrant does the point (9, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  9. 9.What is the midpoint of the line joining (2, 3) and (14, 9)? (a) (6, 3) (b) (16, 12) (c) (8, 6) (d) (6, 8)
  10. 10.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  11. 11.What is the distance between the points (5, 2) and (13, 8)? (a) 10 (b) 14 (c) 11 (d) 100
  12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  13. 13.What is the midpoint of the line joining (8, 6) and (16, 12)? (a) (9, 12) (b) (12, 9) (c) (4, 3) (d) (24, 18)
  14. 14.In which quadrant does the point (−7, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  15. 15.What is the midpoint of the line joining (3, 14) and (15, 4)? (a) (10, 9) (b) (6, 5) (c) (18, 18) (d) (9, 9)
  16. 16.What is the distance between the points (6, 6) and (14, 21)? (a) 18 (b) 23 (c) 17 (d) 289
  17. 17.In which quadrant does the point (−4, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  18. 18.What is the distance between the points (2, 8) and (8, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  19. 19.What is the midpoint of the line joining (1, 0) and (9, 10)? (a) (4, 5) (b) (5, 5) (c) (10, 10) (d) (6, 5)
  20. 20.In which quadrant does the point (3, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  22. 22.What is the distance between the points (4, 12) and (7, 8)? (a) 6 (b) 7 (c) 25 (d) 5
  23. 23.What is the midpoint of the line joining (7, 17) and (19, 9)? (a) (26, 26) (b) (13, 13) (c) (14, 13) (d) (6, 4)
  24. 24.What is the midpoint of the line joining (1, 1) and (3, 5)? (a) (2, 3) (b) (4, 6) (c) (1, 2) (d) (3, 2)
  25. 25.In which quadrant does the point (−4, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  26. 26.What is the distance between the points (2, 5) and (6, 2)? (a) 25 (b) 5 (c) 6 (d) 7
  27. 27.What is the distance between the points (9, 19) and (17, 4)? (a) 289 (b) 23 (c) 17 (d) 18
  28. 28.What is the distance between the points (9, 3) and (16, 27)? (a) 25 (b) 26 (c) 625 (d) 31
  29. 29.What is the distance between the points (6, 0) and (18, 9)? (a) 21 (b) 16 (c) 225 (d) 15
  30. 30.What is the distance between the points (7, 2) and (14, 26)? (a) 625 (b) 25 (c) 31 (d) 26
  31. 31.What is the distance between the points (9, 15) and (33, 8)? (a) 26 (b) 25 (c) 625 (d) 31
  32. 32.In which quadrant does the point (−4, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (2, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  34. 34.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  35. 35.What is the distance between the points (2, 31) and (9, 7)? (a) 31 (b) 26 (c) 25 (d) 625
  36. 36.In which quadrant does the point (1, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  37. 37.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  38. 38.What is the midpoint of the line joining (9, 2) and (11, 12)? (a) (1, 5) (b) (7, 10) (c) (20, 14) (d) (10, 7)
  39. 39.What is the midpoint of the line joining (9, 5) and (13, 11)? (a) (22, 16) (b) (11, 8) (c) (2, 3) (d) (8, 11)
  40. 40.In which quadrant does the point (−5, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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