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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 644 · 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, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  2. 2.What is the midpoint of the line joining (3, 11) and (7, 9)? (a) (10, 20) (b) (2, 1) (c) (5, 10) (d) (10, 5)
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  4. 4.What is the midpoint of the line joining (7, 4) and (15, 0)? (a) (4, 2) (b) (11, 2) (c) (2, 11) (d) (22, 4)
  5. 5.In which quadrant does the point (−8, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  8. 8.In which quadrant does the point (−6, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  9. 9.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  10. 10.In which quadrant does the point (1, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.In which quadrant does the point (9, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  12. 12.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.In which quadrant does the point (−1, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (3, 7) and (6, 3)? (a) 6 (b) 25 (c) 7 (d) 5
  15. 15.In which quadrant does the point (6, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  17. 17.What is the distance between the points (4, 9) and (28, 16)? (a) 26 (b) 31 (c) 625 (d) 25
  18. 18.What is the distance between the points (0, 0) and (24, 7)? (a) 625 (b) 25 (c) 31 (d) 26
  19. 19.What is the distance between the points (9, 7) and (25, 19)? (a) 20 (b) 21 (c) 28 (d) 400
  20. 20.What is the distance between the points (1, 11) and (4, 7)? (a) 25 (b) 5 (c) 6 (d) 7
  21. 21.In which quadrant does the point (−1, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  22. 22.What is the midpoint of the line joining (9, 0) and (15, 10)? (a) (24, 10) (b) (12, 5) (c) (3, 5) (d) (5, 12)
  23. 23.In which quadrant does the point (−1, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  24. 24.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  25. 25.What is the midpoint of the line joining (3, 10) and (13, 18)? (a) (8, 14) (b) (5, 4) (c) (16, 28) (d) (14, 8)
  26. 26.In which quadrant does the point (−5, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.In which quadrant does the point (−7, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (0, 3) and (8, 15)? (a) (4, 6) (b) (4, 9) (c) (8, 18) (d) (9, 4)
  29. 29.In which quadrant does the point (−4, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.What is the midpoint of the line joining (2, 9) and (6, 17)? (a) (2, 4) (b) (4, 13) (c) (8, 26) (d) (13, 4)
  31. 31.In which quadrant does the point (−3, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.What is the midpoint of the line joining (0, 22) and (2, 10)? (a) (16, 1) (b) (1, 16) (c) (2, 32) (d) (1, 6)
  33. 33.In which quadrant does the point (−6, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  35. 35.What is the midpoint of the line joining (5, 9) and (11, 5)? (a) (7, 8) (b) (3, 2) (c) (8, 7) (d) (16, 14)
  36. 36.What is the distance between the points (4, 17) and (20, 5)? (a) 20 (b) 28 (c) 400 (d) 21
  37. 37.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  38. 38.In which quadrant does the point (6, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  40. 40.What is the midpoint of the line joining (1, 1) and (9, 13)? (a) (10, 14) (b) (7, 5) (c) (4, 6) (d) (5, 7)

Answer key

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

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