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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 483 · 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 (5, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  4. 4.What is the midpoint of the line joining (2, 18) and (14, 6)? (a) (6, 6) (b) (16, 24) (c) (8, 12) (d) (12, 8)
  5. 5.What is the midpoint of the line joining (7, 4) and (15, 10)? (a) (22, 14) (b) (11, 7) (c) (7, 11) (d) (4, 3)
  6. 6.In which quadrant does the point (2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the distance between the points (6, 8) and (14, 14)? (a) 100 (b) 10 (c) 14 (d) 11
  8. 8.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  9. 9.What is the midpoint of the line joining (6, 9) and (12, 13)? (a) (3, 2) (b) (9, 11) (c) (11, 9) (d) (18, 22)
  10. 10.What is the distance between the points (1, 5) and (8, 29)? (a) 26 (b) 31 (c) 25 (d) 625
  11. 11.What is the distance between the points (2, 15) and (7, 3)? (a) 14 (b) 17 (c) 169 (d) 13
  12. 12.In which quadrant does the point (−3, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  13. 13.In which quadrant does the point (−4, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the distance between the points (0, 8) and (15, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  15. 15.What is the midpoint of the line joining (7, 1) and (17, 7)? (a) (4, 12) (b) (5, 3) (c) (12, 4) (d) (24, 8)
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  17. 17.In which quadrant does the point (2, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  18. 18.What is the midpoint of the line joining (0, 16) and (8, 4)? (a) (8, 20) (b) (4, 10) (c) (10, 4) (d) (4, 6)
  19. 19.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  20. 20.In which quadrant does the point (4, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  21. 21.What is the distance between the points (5, 2) and (29, 9)? (a) 625 (b) 26 (c) 31 (d) 25
  22. 22.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  23. 23.What is the distance between the points (5, 13) and (8, 9)? (a) 7 (b) 25 (c) 5 (d) 6
  24. 24.What is the midpoint of the line joining (3, 7) and (5, 19)? (a) (13, 4) (b) (1, 6) (c) (8, 26) (d) (4, 13)
  25. 25.In which quadrant does the point (8, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  26. 26.In which quadrant does the point (−9, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  27. 27.What is the midpoint of the line joining (3, 3) and (7, 11)? (a) (5, 7) (b) (10, 14) (c) (7, 5) (d) (2, 4)
  28. 28.What is the midpoint of the line joining (2, 12) and (4, 10)? (a) (1, 1) (b) (11, 3) (c) (6, 22) (d) (3, 11)
  29. 29.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  30. 30.What is the distance between the points (3, 17) and (18, 9)? (a) 17 (b) 18 (c) 23 (d) 289
  31. 31.What is the midpoint of the line joining (10, 1) and (12, 3)? (a) (11, 2) (b) (1, 1) (c) (22, 4) (d) (2, 11)
  32. 32.What is the distance between the points (6, 1) and (11, 13)? (a) 13 (b) 169 (c) 14 (d) 17
  33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  34. 34.What is the distance between the points (9, 0) and (14, 12)? (a) 14 (b) 13 (c) 17 (d) 169
  35. 35.What is the midpoint of the line joining (9, 11) and (13, 9)? (a) (2, 1) (b) (22, 20) (c) (11, 10) (d) (10, 11)
  36. 36.What is the distance between the points (8, 12) and (24, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  37. 37.In which quadrant does the point (5, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  38. 38.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  39. 39.What is the distance between the points (0, 18) and (9, 6)? (a) 15 (b) 225 (c) 16 (d) 21
  40. 40.What is the midpoint of the line joining (6, 17) and (14, 5)? (a) (20, 22) (b) (11, 10) (c) (4, 6) (d) (10, 11)

Answer key

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

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