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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 798 · 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 (6, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (7, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  4. 4.What is the distance between the points (3, 20) and (19, 8)? (a) 28 (b) 21 (c) 20 (d) 400
  5. 5.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  6. 6.What is the midpoint of the line joining (1, 9) and (13, 11)? (a) (14, 20) (b) (6, 1) (c) (7, 10) (d) (10, 7)
  7. 7.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  8. 8.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  9. 9.What is the distance between the points (0, 12) and (3, 8)? (a) 5 (b) 25 (c) 6 (d) 7
  10. 10.What is the distance between the points (4, 19) and (13, 7)? (a) 16 (b) 21 (c) 15 (d) 225
  11. 11.What is the distance between the points (2, 8) and (8, 16)? (a) 10 (b) 100 (c) 14 (d) 11
  12. 12.What is the midpoint of the line joining (9, 12) and (21, 4)? (a) (30, 16) (b) (6, 4) (c) (8, 15) (d) (15, 8)
  13. 13.What is the midpoint of the line joining (5, 5) and (17, 1)? (a) (3, 11) (b) (22, 6) (c) (6, 2) (d) (11, 3)
  14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  15. 15.What is the distance between the points (9, 1) and (15, 9)? (a) 14 (b) 10 (c) 100 (d) 11
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  17. 17.In which quadrant does the point (−7, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  18. 18.What is the midpoint of the line joining (7, 11) and (19, 1)? (a) (6, 5) (b) (6, 13) (c) (26, 12) (d) (13, 6)
  19. 19.In which quadrant does the point (5, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  20. 20.What is the distance between the points (3, 18) and (15, 2)? (a) 21 (b) 28 (c) 20 (d) 400
  21. 21.In which quadrant does the point (−6, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  22. 22.What is the distance between the points (9, 9) and (14, 21)? (a) 13 (b) 17 (c) 14 (d) 169
  23. 23.What is the midpoint of the line joining (6, 2) and (10, 12)? (a) (8, 7) (b) (16, 14) (c) (7, 8) (d) (2, 5)
  24. 24.In which quadrant does the point (−9, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  26. 26.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.What is the midpoint of the line joining (5, 8) and (9, 12)? (a) (2, 2) (b) (10, 7) (c) (14, 20) (d) (7, 10)
  28. 28.In which quadrant does the point (1, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.What is the distance between the points (9, 4) and (21, 20)? (a) 28 (b) 400 (c) 21 (d) 20
  30. 30.What is the distance between the points (8, 8) and (32, 1)? (a) 25 (b) 26 (c) 625 (d) 31
  31. 31.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  32. 32.What is the distance between the points (8, 2) and (24, 14)? (a) 400 (b) 21 (c) 20 (d) 28
  33. 33.In which quadrant does the point (−1, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.What is the distance between the points (0, 5) and (9, 17)? (a) 225 (b) 16 (c) 15 (d) 21
  35. 35.In which quadrant does the point (9, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  37. 37.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (−9, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  39. 39.In which quadrant does the point (−3, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.In which quadrant does the point (9, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant

Answer key

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

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