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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 968 · 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 (−2, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  2. 2.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.What is the midpoint of the line joining (1, 0) and (5, 2)? (a) (6, 2) (b) (3, 1) (c) (1, 3) (d) (2, 1)
  4. 4.In which quadrant does the point (8, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.What is the distance between the points (2, 0) and (6, 3)? (a) 6 (b) 25 (c) 7 (d) 5
  6. 6.What is the midpoint of the line joining (2, 13) and (4, 1)? (a) (6, 14) (b) (7, 3) (c) (1, 6) (d) (3, 7)
  7. 7.What is the midpoint of the line joining (8, 6) and (18, 8)? (a) (13, 7) (b) (5, 1) (c) (26, 14) (d) (7, 13)
  8. 8.What is the midpoint of the line joining (7, 15) and (13, 5)? (a) (10, 10) (b) (3, 5) (c) (11, 10) (d) (20, 20)
  9. 9.In which quadrant does the point (3, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  10. 10.In which quadrant does the point (−9, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  11. 11.What is the distance between the points (7, 12) and (19, 7)? (a) 13 (b) 14 (c) 17 (d) 169
  12. 12.In which quadrant does the point (2, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (2, 9) and (6, 7)? (a) (4, 8) (b) (8, 4) (c) (2, 1) (d) (8, 16)
  14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  15. 15.What is the distance between the points (0, 3) and (6, 11)? (a) 10 (b) 100 (c) 11 (d) 14
  16. 16.What is the distance between the points (0, 7) and (12, 16)? (a) 21 (b) 16 (c) 225 (d) 15
  17. 17.What is the distance between the points (7, 12) and (16, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  18. 18.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  20. 20.What is the distance between the points (1, 10) and (13, 1)? (a) 15 (b) 16 (c) 21 (d) 225
  21. 21.What is the distance between the points (2, 8) and (10, 23)? (a) 23 (b) 18 (c) 17 (d) 289
  22. 22.In which quadrant does the point (3, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  23. 23.What is the midpoint of the line joining (2, 18) and (6, 6)? (a) (4, 12) (b) (8, 24) (c) (2, 6) (d) (12, 4)
  24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  25. 25.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (10, 9) and (14, 13)? (a) (2, 2) (b) (12, 11) (c) (24, 22) (d) (11, 12)
  27. 27.What is the distance between the points (0, 5) and (6, 13)? (a) 10 (b) 14 (c) 100 (d) 11
  28. 28.In which quadrant does the point (4, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  29. 29.What is the midpoint of the line joining (3, 22) and (9, 10)? (a) (16, 6) (b) (3, 6) (c) (12, 32) (d) (6, 16)
  30. 30.What is the midpoint of the line joining (1, 10) and (5, 4)? (a) (3, 7) (b) (2, 3) (c) (7, 3) (d) (6, 14)
  31. 31.In which quadrant does the point (2, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  32. 32.What is the distance between the points (9, 4) and (13, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  33. 33.What is the distance between the points (6, 18) and (18, 9)? (a) 15 (b) 225 (c) 21 (d) 16
  34. 34.What is the distance between the points (1, 25) and (13, 9)? (a) 28 (b) 400 (c) 20 (d) 21
  35. 35.What is the distance between the points (5, 13) and (11, 5)? (a) 100 (b) 11 (c) 10 (d) 14
  36. 36.What is the midpoint of the line joining (0, 0) and (8, 8)? (a) (4, 4) (b) (4, 5) (c) (8, 8) (d) (5, 4)
  37. 37.What is the midpoint of the line joining (4, 16) and (8, 8)? (a) (12, 6) (b) (12, 24) (c) (2, 4) (d) (6, 12)
  38. 38.In which quadrant does the point (3, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  39. 39.What is the midpoint of the line joining (0, 0) and (2, 10)? (a) (5, 1) (b) (2, 10) (c) (2, 5) (d) (1, 5)
  40. 40.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17

Answer key

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

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