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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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