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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 276 · 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 (3, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  2. 2.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  3. 3.What is the distance between the points (8, 28) and (15, 4)? (a) 25 (b) 26 (c) 31 (d) 625
  4. 4.What is the distance between the points (6, 12) and (12, 4)? (a) 14 (b) 11 (c) 10 (d) 100
  5. 5.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  6. 6.In which quadrant does the point (−2, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  7. 7.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  9. 9.What is the midpoint of the line joining (8, 15) and (20, 9)? (a) (6, 3) (b) (12, 14) (c) (14, 12) (d) (28, 24)
  10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  12. 12.What is the distance between the points (6, 1) and (21, 9)? (a) 23 (b) 18 (c) 289 (d) 17
  13. 13.What is the distance between the points (0, 5) and (15, 13)? (a) 23 (b) 17 (c) 18 (d) 289
  14. 14.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  15. 15.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  16. 16.What is the midpoint of the line joining (1, 3) and (13, 5)? (a) (4, 7) (b) (6, 1) (c) (7, 4) (d) (14, 8)
  17. 17.What is the midpoint of the line joining (3, 8) and (9, 16)? (a) (12, 6) (b) (12, 24) (c) (3, 4) (d) (6, 12)
  18. 18.What is the distance between the points (5, 8) and (20, 16)? (a) 23 (b) 289 (c) 18 (d) 17
  19. 19.What is the distance between the points (5, 10) and (17, 1)? (a) 21 (b) 16 (c) 15 (d) 225
  20. 20.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  21. 21.What is the distance between the points (4, 8) and (28, 1)? (a) 26 (b) 25 (c) 625 (d) 31
  22. 22.What is the distance between the points (1, 16) and (13, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  23. 23.What is the distance between the points (5, 4) and (10, 16)? (a) 13 (b) 17 (c) 169 (d) 14
  24. 24.What is the midpoint of the line joining (6, 6) and (10, 8)? (a) (7, 8) (b) (8, 7) (c) (16, 14) (d) (2, 1)
  25. 25.What is the distance between the points (9, 9) and (24, 1)? (a) 17 (b) 23 (c) 289 (d) 18
  26. 26.What is the distance between the points (2, 9) and (14, 18)? (a) 15 (b) 21 (c) 225 (d) 16
  27. 27.What is the midpoint of the line joining (2, 3) and (4, 5)? (a) (1, 1) (b) (4, 3) (c) (6, 8) (d) (3, 4)
  28. 28.What is the midpoint of the line joining (9, 8) and (13, 10)? (a) (11, 9) (b) (9, 11) (c) (2, 1) (d) (22, 18)
  29. 29.What is the distance between the points (6, 5) and (14, 11)? (a) 11 (b) 10 (c) 14 (d) 100
  30. 30.What is the distance between the points (1, 4) and (13, 20)? (a) 400 (b) 21 (c) 20 (d) 28
  31. 31.In which quadrant does the point (6, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the distance between the points (4, 24) and (16, 8)? (a) 28 (b) 20 (c) 400 (d) 21
  33. 33.What is the distance between the points (5, 2) and (12, 26)? (a) 625 (b) 31 (c) 26 (d) 25
  34. 34.What is the midpoint of the line joining (1, 11) and (3, 7)? (a) (9, 2) (b) (2, 9) (c) (1, 2) (d) (4, 18)
  35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  39. 39.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.In which quadrant does the point (−1, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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