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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 804 · 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 (7, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  2. 2.What is the midpoint of the line joining (10, 8) and (18, 6)? (a) (4, 1) (b) (28, 14) (c) (14, 7) (d) (7, 14)
  3. 3.What is the distance between the points (0, 1) and (8, 7)? (a) 100 (b) 10 (c) 11 (d) 14
  4. 4.What is the distance between the points (9, 9) and (25, 21)? (a) 20 (b) 400 (c) 21 (d) 28
  5. 5.What is the midpoint of the line joining (9, 9) and (17, 5)? (a) (4, 2) (b) (7, 13) (c) (26, 14) (d) (13, 7)
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  7. 7.What is the distance between the points (7, 12) and (13, 4)? (a) 100 (b) 11 (c) 14 (d) 10
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  9. 9.What is the distance between the points (7, 17) and (23, 5)? (a) 400 (b) 20 (c) 28 (d) 21
  10. 10.What is the midpoint of the line joining (4, 6) and (8, 0)? (a) (6, 3) (b) (3, 6) (c) (12, 6) (d) (2, 3)
  11. 11.What is the midpoint of the line joining (6, 7) and (16, 5)? (a) (11, 6) (b) (22, 12) (c) (6, 11) (d) (5, 1)
  12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  14. 14.What is the distance between the points (4, 10) and (10, 2)? (a) 100 (b) 10 (c) 11 (d) 14
  15. 15.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  16. 16.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.What is the distance between the points (6, 6) and (9, 2)? (a) 25 (b) 7 (c) 6 (d) 5
  18. 18.In which quadrant does the point (−1, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.What is the midpoint of the line joining (7, 9) and (19, 21)? (a) (15, 13) (b) (13, 15) (c) (6, 6) (d) (26, 30)
  20. 20.What is the distance between the points (6, 11) and (9, 7)? (a) 6 (b) 25 (c) 5 (d) 7
  21. 21.In which quadrant does the point (−4, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (8, 5) and (10, 13)? (a) (1, 4) (b) (18, 18) (c) (10, 9) (d) (9, 9)
  23. 23.In which quadrant does the point (5, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  24. 24.What is the midpoint of the line joining (5, 9) and (11, 7)? (a) (9, 8) (b) (3, 1) (c) (8, 8) (d) (16, 16)
  25. 25.What is the midpoint of the line joining (2, 9) and (6, 5)? (a) (7, 4) (b) (8, 14) (c) (2, 2) (d) (4, 7)
  26. 26.In which quadrant does the point (5, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.In which quadrant does the point (−5, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  28. 28.What is the midpoint of the line joining (1, 6) and (9, 4)? (a) (10, 10) (b) (5, 5) (c) (6, 5) (d) (4, 1)
  29. 29.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (9, 6) and (17, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  31. 31.What is the distance between the points (5, 9) and (13, 24)? (a) 23 (b) 289 (c) 18 (d) 17
  32. 32.What is the midpoint of the line joining (8, 3) and (12, 13)? (a) (20, 16) (b) (8, 10) (c) (2, 5) (d) (10, 8)
  33. 33.What is the midpoint of the line joining (2, 4) and (8, 12)? (a) (8, 5) (b) (5, 8) (c) (10, 16) (d) (3, 4)
  34. 34.In which quadrant does the point (2, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.What is the distance between the points (0, 13) and (12, 8)? (a) 17 (b) 13 (c) 169 (d) 14
  36. 36.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  37. 37.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  38. 38.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  40. 40.What is the distance between the points (4, 7) and (11, 31)? (a) 26 (b) 625 (c) 31 (d) 25

Answer key

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

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