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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 282 · 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 (8, 4) and (18, 8)? (a) (5, 2) (b) (26, 12) (c) (13, 6) (d) (6, 13)
  2. 2.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  4. 4.In which quadrant does the point (−2, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.In which quadrant does the point (−5, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  6. 6.In which quadrant does the point (5, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.What is the midpoint of the line joining (0, 15) and (12, 9)? (a) (6, 3) (b) (12, 24) (c) (12, 6) (d) (6, 12)
  8. 8.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  9. 9.What is the midpoint of the line joining (3, 10) and (15, 4)? (a) (18, 14) (b) (9, 7) (c) (7, 9) (d) (6, 3)
  10. 10.What is the distance between the points (7, 19) and (16, 7)? (a) 16 (b) 15 (c) 225 (d) 21
  11. 11.What is the distance between the points (1, 9) and (9, 3)? (a) 100 (b) 10 (c) 11 (d) 14
  12. 12.What is the distance between the points (5, 2) and (14, 14)? (a) 16 (b) 15 (c) 225 (d) 21
  13. 13.What is the distance between the points (7, 14) and (16, 2)? (a) 21 (b) 15 (c) 225 (d) 16
  14. 14.What is the midpoint of the line joining (0, 0) and (8, 12)? (a) (5, 6) (b) (6, 4) (c) (4, 6) (d) (8, 12)
  15. 15.In which quadrant does the point (−1, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  16. 16.What is the distance between the points (1, 15) and (16, 7)? (a) 23 (b) 18 (c) 17 (d) 289
  17. 17.What is the midpoint of the line joining (5, 3) and (13, 5)? (a) (4, 1) (b) (18, 8) (c) (4, 9) (d) (9, 4)
  18. 18.What is the midpoint of the line joining (4, 1) and (10, 7)? (a) (7, 4) (b) (4, 7) (c) (3, 3) (d) (14, 8)
  19. 19.What is the midpoint of the line joining (1, 11) and (3, 3)? (a) (4, 14) (b) (1, 4) (c) (7, 2) (d) (2, 7)
  20. 20.What is the distance between the points (5, 18) and (17, 9)? (a) 16 (b) 21 (c) 15 (d) 225
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  22. 22.What is the distance between the points (9, 14) and (18, 2)? (a) 225 (b) 21 (c) 16 (d) 15
  23. 23.In which quadrant does the point (8, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.In which quadrant does the point (1, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.What is the distance between the points (5, 13) and (20, 5)? (a) 23 (b) 18 (c) 289 (d) 17
  26. 26.In which quadrant does the point (−4, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  28. 28.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  29. 29.What is the distance between the points (5, 8) and (29, 1)? (a) 625 (b) 26 (c) 25 (d) 31
  30. 30.What is the midpoint of the line joining (7, 10) and (19, 8)? (a) (6, 1) (b) (9, 13) (c) (13, 9) (d) (26, 18)
  31. 31.In which quadrant does the point (−7, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  32. 32.What is the distance between the points (0, 5) and (3, 9)? (a) 25 (b) 7 (c) 6 (d) 5
  33. 33.What is the midpoint of the line joining (3, 16) and (15, 8)? (a) (6, 4) (b) (12, 9) (c) (9, 12) (d) (18, 24)
  34. 34.What is the distance between the points (4, 2) and (16, 18)? (a) 400 (b) 21 (c) 28 (d) 20
  35. 35.In which quadrant does the point (7, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  36. 36.What is the midpoint of the line joining (3, 3) and (15, 7)? (a) (18, 10) (b) (9, 5) (c) (5, 9) (d) (6, 2)
  37. 37.In which quadrant does the point (9, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the midpoint of the line joining (7, 15) and (19, 3)? (a) (9, 13) (b) (6, 6) (c) (13, 9) (d) (26, 18)
  39. 39.What is the midpoint of the line joining (9, 6) and (17, 0)? (a) (26, 6) (b) (4, 3) (c) (3, 13) (d) (13, 3)
  40. 40.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18

Answer key

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

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