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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 952 · 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 midpoint of the line joining (10, 16) and (18, 10)? (a) (14, 13) (b) (28, 26) (c) (4, 3) (d) (13, 14)
  2. 2.What is the midpoint of the line joining (10, 10) and (16, 0)? (a) (5, 13) (b) (3, 5) (c) (13, 5) (d) (26, 10)
  3. 3.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the midpoint of the line joining (6, 1) and (8, 5)? (a) (14, 6) (b) (1, 2) (c) (3, 7) (d) (7, 3)
  5. 5.In which quadrant does the point (3, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.In which quadrant does the point (1, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.In which quadrant does the point (4, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  8. 8.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  11. 11.What is the midpoint of the line joining (0, 5) and (2, 7)? (a) (1, 1) (b) (1, 6) (c) (6, 1) (d) (2, 12)
  12. 12.In which quadrant does the point (−4, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.What is the midpoint of the line joining (0, 2) and (12, 0)? (a) (6, 1) (b) (12, 2) (c) (7, 1) (d) (1, 6)
  14. 14.What is the distance between the points (6, 0) and (14, 6)? (a) 14 (b) 11 (c) 100 (d) 10
  15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  16. 16.In which quadrant does the point (9, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  17. 17.What is the distance between the points (6, 7) and (13, 31)? (a) 26 (b) 31 (c) 25 (d) 625
  18. 18.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  19. 19.In which quadrant does the point (7, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  21. 21.What is the distance between the points (4, 9) and (9, 21)? (a) 17 (b) 14 (c) 13 (d) 169
  22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  23. 23.In which quadrant does the point (−4, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.What is the midpoint of the line joining (10, 7) and (22, 5)? (a) (32, 12) (b) (16, 6) (c) (6, 16) (d) (6, 1)
  25. 25.What is the distance between the points (0, 5) and (16, 17)? (a) 21 (b) 28 (c) 400 (d) 20
  26. 26.What is the distance between the points (9, 1) and (24, 9)? (a) 17 (b) 18 (c) 289 (d) 23
  27. 27.In which quadrant does the point (−8, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  28. 28.What is the distance between the points (2, 22) and (14, 6)? (a) 20 (b) 400 (c) 28 (d) 21
  29. 29.In which quadrant does the point (−3, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  30. 30.In which quadrant does the point (−1, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  32. 32.What is the distance between the points (1, 5) and (17, 17)? (a) 400 (b) 20 (c) 28 (d) 21
  33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  34. 34.What is the distance between the points (2, 1) and (17, 9)? (a) 289 (b) 18 (c) 23 (d) 17
  35. 35.In which quadrant does the point (−3, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the distance between the points (7, 13) and (19, 8)? (a) 169 (b) 17 (c) 13 (d) 14
  37. 37.What is the distance between the points (0, 16) and (16, 4)? (a) 20 (b) 21 (c) 28 (d) 400
  38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  39. 39.What is the distance between the points (9, 2) and (21, 18)? (a) 400 (b) 20 (c) 28 (d) 21
  40. 40.In which quadrant does the point (9, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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