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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 898 · 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, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  3. 3.What is the distance between the points (2, 17) and (18, 5)? (a) 21 (b) 20 (c) 28 (d) 400
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  6. 6.What is the distance between the points (6, 3) and (9, 7)? (a) 25 (b) 7 (c) 5 (d) 6
  7. 7.What is the distance between the points (5, 8) and (13, 2)? (a) 10 (b) 11 (c) 14 (d) 100
  8. 8.What is the distance between the points (0, 0) and (12, 16)? (a) 28 (b) 21 (c) 20 (d) 400
  9. 9.What is the distance between the points (3, 15) and (11, 9)? (a) 11 (b) 100 (c) 10 (d) 14
  10. 10.In which quadrant does the point (5, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  12. 12.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  13. 13.What is the distance between the points (7, 13) and (23, 1)? (a) 28 (b) 400 (c) 20 (d) 21
  14. 14.What is the midpoint of the line joining (2, 9) and (8, 11)? (a) (3, 1) (b) (5, 10) (c) (10, 20) (d) (10, 5)
  15. 15.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (3, 12) and (11, 2)? (a) (4, 5) (b) (8, 7) (c) (7, 7) (d) (14, 14)
  17. 17.In which quadrant does the point (6, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  20. 20.What is the distance between the points (3, 17) and (15, 1)? (a) 28 (b) 400 (c) 20 (d) 21
  21. 21.In which quadrant does the point (−1, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  22. 22.In which quadrant does the point (7, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  23. 23.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  24. 24.What is the midpoint of the line joining (1, 7) and (9, 15)? (a) (11, 5) (b) (4, 4) (c) (10, 22) (d) (5, 11)
  25. 25.What is the midpoint of the line joining (8, 7) and (18, 15)? (a) (13, 11) (b) (11, 13) (c) (5, 4) (d) (26, 22)
  26. 26.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  27. 27.What is the midpoint of the line joining (10, 12) and (22, 8)? (a) (6, 2) (b) (10, 16) (c) (16, 10) (d) (32, 20)
  28. 28.In which quadrant does the point (−1, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  30. 30.What is the midpoint of the line joining (9, 7) and (11, 17)? (a) (12, 10) (b) (20, 24) (c) (10, 12) (d) (1, 5)
  31. 31.What is the midpoint of the line joining (1, 17) and (7, 5)? (a) (3, 6) (b) (11, 4) (c) (8, 22) (d) (4, 11)
  32. 32.What is the midpoint of the line joining (1, 1) and (9, 13)? (a) (4, 6) (b) (7, 5) (c) (5, 7) (d) (10, 14)
  33. 33.What is the midpoint of the line joining (5, 5) and (7, 15)? (a) (12, 20) (b) (1, 5) (c) (6, 10) (d) (10, 6)
  34. 34.In which quadrant does the point (−4, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  35. 35.What is the midpoint of the line joining (9, 12) and (17, 6)? (a) (4, 3) (b) (9, 13) (c) (26, 18) (d) (13, 9)
  36. 36.What is the distance between the points (3, 0) and (7, 3)? (a) 5 (b) 6 (c) 7 (d) 25
  37. 37.In which quadrant does the point (−9, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  38. 38.In which quadrant does the point (−7, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.What is the midpoint of the line joining (0, 10) and (12, 22)? (a) (6, 6) (b) (12, 32) (c) (16, 6) (d) (6, 16)
  40. 40.What is the distance between the points (6, 6) and (21, 14)? (a) 17 (b) 23 (c) 289 (d) 18

Answer key

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

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