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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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