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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 567 · 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 (8, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (4, 6) and (13, 18)? (a) 16 (b) 225 (c) 21 (d) 15
  3. 3.In which quadrant does the point (−3, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  4. 4.What is the distance between the points (9, 4) and (24, 12)? (a) 23 (b) 18 (c) 17 (d) 289
  5. 5.What is the midpoint of the line joining (2, 13) and (8, 7)? (a) (3, 3) (b) (10, 5) (c) (10, 20) (d) (5, 10)
  6. 6.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  7. 7.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  8. 8.In which quadrant does the point (6, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  10. 10.What is the distance between the points (6, 15) and (14, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  11. 11.What is the midpoint of the line joining (8, 0) and (18, 10)? (a) (5, 5) (b) (13, 5) (c) (5, 13) (d) (26, 10)
  12. 12.What is the midpoint of the line joining (1, 22) and (13, 10)? (a) (6, 6) (b) (7, 16) (c) (14, 32) (d) (16, 7)
  13. 13.What is the distance between the points (2, 20) and (14, 4)? (a) 400 (b) 20 (c) 28 (d) 21
  14. 14.In which quadrant does the point (−6, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.In which quadrant does the point (4, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  16. 16.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  19. 19.What is the distance between the points (0, 4) and (3, 8)? (a) 6 (b) 7 (c) 25 (d) 5
  20. 20.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  21. 21.In which quadrant does the point (−7, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  22. 22.What is the midpoint of the line joining (7, 5) and (15, 3)? (a) (11, 4) (b) (22, 8) (c) (4, 11) (d) (4, 1)
  23. 23.What is the midpoint of the line joining (6, 12) and (14, 6)? (a) (20, 18) (b) (4, 3) (c) (10, 9) (d) (9, 10)
  24. 24.What is the distance between the points (2, 6) and (10, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  25. 25.What is the midpoint of the line joining (0, 0) and (12, 10)? (a) (5, 6) (b) (12, 10) (c) (7, 5) (d) (6, 5)
  26. 26.What is the midpoint of the line joining (3, 17) and (15, 7)? (a) (6, 5) (b) (9, 12) (c) (12, 9) (d) (18, 24)
  27. 27.What is the distance between the points (2, 10) and (6, 7)? (a) 25 (b) 6 (c) 7 (d) 5
  28. 28.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−4, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  30. 30.What is the midpoint of the line joining (0, 1) and (8, 5)? (a) (4, 2) (b) (4, 3) (c) (8, 6) (d) (3, 4)
  31. 31.In which quadrant does the point (8, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the distance between the points (0, 1) and (12, 10)? (a) 16 (b) 21 (c) 225 (d) 15
  33. 33.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  34. 34.What is the midpoint of the line joining (5, 22) and (9, 10)? (a) (2, 6) (b) (14, 32) (c) (7, 16) (d) (16, 7)
  35. 35.What is the midpoint of the line joining (8, 7) and (14, 1)? (a) (11, 4) (b) (22, 8) (c) (4, 11) (d) (3, 3)
  36. 36.What is the distance between the points (6, 2) and (15, 14)? (a) 15 (b) 225 (c) 21 (d) 16
  37. 37.What is the midpoint of the line joining (6, 1) and (8, 13)? (a) (14, 14) (b) (1, 6) (c) (7, 7) (d) (8, 7)
  38. 38.In which quadrant does the point (−9, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.In which quadrant does the point (3, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (6, 9) and (9, 13)? (a) 6 (b) 7 (c) 25 (d) 5

Answer key

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

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