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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 351 · 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.What is the distance between the points (4, 16) and (12, 1)? (a) 23 (b) 18 (c) 289 (d) 17
  2. 2.In which quadrant does the point (−2, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.In which quadrant does the point (−4, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  4. 4.What is the distance between the points (3, 13) and (18, 5)? (a) 17 (b) 18 (c) 23 (d) 289
  5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  6. 6.In which quadrant does the point (3, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  7. 7.In which quadrant does the point (−2, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (0, 4) and (9, 16)? (a) 225 (b) 21 (c) 15 (d) 16
  9. 9.What is the midpoint of the line joining (6, 3) and (12, 7)? (a) (3, 2) (b) (18, 10) (c) (9, 5) (d) (5, 9)
  10. 10.What is the midpoint of the line joining (1, 9) and (3, 21)? (a) (2, 15) (b) (15, 2) (c) (4, 30) (d) (1, 6)
  11. 11.What is the midpoint of the line joining (4, 6) and (10, 18)? (a) (3, 6) (b) (12, 7) (c) (14, 24) (d) (7, 12)
  12. 12.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  13. 13.What is the midpoint of the line joining (5, 5) and (7, 11)? (a) (1, 3) (b) (6, 8) (c) (8, 6) (d) (12, 16)
  14. 14.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  15. 15.What is the distance between the points (8, 7) and (16, 1)? (a) 10 (b) 100 (c) 14 (d) 11
  16. 16.What is the midpoint of the line joining (5, 7) and (15, 13)? (a) (5, 3) (b) (10, 10) (c) (20, 20) (d) (11, 10)
  17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  18. 18.What is the midpoint of the line joining (9, 7) and (17, 15)? (a) (11, 13) (b) (26, 22) (c) (4, 4) (d) (13, 11)
  19. 19.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  20. 20.In which quadrant does the point (−9, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (9, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.In which quadrant does the point (1, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  23. 23.What is the distance between the points (1, 4) and (4, 8)? (a) 25 (b) 7 (c) 6 (d) 5
  24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  26. 26.What is the distance between the points (5, 17) and (14, 5)? (a) 21 (b) 16 (c) 225 (d) 15
  27. 27.What is the midpoint of the line joining (9, 4) and (15, 2)? (a) (3, 12) (b) (12, 3) (c) (24, 6) (d) (3, 1)
  28. 28.In which quadrant does the point (9, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (6, 7) and (18, 3)? (a) (12, 5) (b) (24, 10) (c) (5, 12) (d) (6, 2)
  31. 31.In which quadrant does the point (−8, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  32. 32.What is the distance between the points (8, 13) and (20, 4)? (a) 225 (b) 21 (c) 15 (d) 16
  33. 33.What is the midpoint of the line joining (9, 11) and (17, 1)? (a) (26, 12) (b) (13, 6) (c) (6, 13) (d) (4, 5)
  34. 34.What is the distance between the points (6, 1) and (10, 4)? (a) 5 (b) 6 (c) 25 (d) 7
  35. 35.What is the distance between the points (8, 3) and (16, 9)? (a) 14 (b) 11 (c) 100 (d) 10
  36. 36.What is the distance between the points (0, 11) and (4, 8)? (a) 7 (b) 25 (c) 5 (d) 6
  37. 37.In which quadrant does the point (−3, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (7, 12) and (15, 6)? (a) 11 (b) 10 (c) 100 (d) 14
  39. 39.In which quadrant does the point (3, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31

Answer key

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

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