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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 395 · 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.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  2. 2.In which quadrant does the point (3, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  5. 5.What is the distance between the points (4, 5) and (12, 20)? (a) 289 (b) 18 (c) 17 (d) 23
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  7. 7.In which quadrant does the point (−5, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.In which quadrant does the point (−8, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  9. 9.In which quadrant does the point (−5, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.In which quadrant does the point (−3, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.What is the midpoint of the line joining (8, 10) and (20, 0)? (a) (5, 14) (b) (28, 10) (c) (14, 5) (d) (6, 5)
  12. 12.In which quadrant does the point (6, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  13. 13.In which quadrant does the point (−3, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (10, 9) and (16, 17)? (a) (26, 26) (b) (13, 13) (c) (14, 13) (d) (3, 4)
  15. 15.In which quadrant does the point (−3, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.In which quadrant does the point (−7, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the distance between the points (0, 5) and (12, 21)? (a) 21 (b) 400 (c) 20 (d) 28
  18. 18.What is the distance between the points (1, 12) and (9, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  19. 19.What is the midpoint of the line joining (7, 13) and (15, 5)? (a) (22, 18) (b) (9, 11) (c) (4, 4) (d) (11, 9)
  20. 20.What is the distance between the points (0, 5) and (4, 2)? (a) 25 (b) 6 (c) 7 (d) 5
  21. 21.In which quadrant does the point (−3, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  23. 23.In which quadrant does the point (7, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (−4, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (6, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In which quadrant does the point (3, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.What is the distance between the points (4, 15) and (12, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  28. 28.What is the distance between the points (8, 8) and (11, 12)? (a) 7 (b) 6 (c) 5 (d) 25
  29. 29.In which quadrant does the point (7, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.What is the midpoint of the line joining (8, 5) and (12, 1)? (a) (10, 3) (b) (3, 10) (c) (20, 6) (d) (2, 2)
  31. 31.In which quadrant does the point (−1, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  32. 32.What is the distance between the points (2, 8) and (8, 16)? (a) 11 (b) 100 (c) 14 (d) 10
  33. 33.What is the distance between the points (3, 4) and (15, 13)? (a) 15 (b) 16 (c) 225 (d) 21
  34. 34.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  35. 35.In which quadrant does the point (−2, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (6, 18) and (18, 2)? (a) 28 (b) 400 (c) 20 (d) 21
  37. 37.What is the distance between the points (1, 4) and (8, 28)? (a) 625 (b) 25 (c) 31 (d) 26
  38. 38.What is the distance between the points (8, 7) and (20, 16)? (a) 21 (b) 16 (c) 225 (d) 15
  39. 39.What is the midpoint of the line joining (5, 8) and (11, 6)? (a) (16, 14) (b) (8, 7) (c) (7, 8) (d) (3, 1)
  40. 40.What is the distance between the points (0, 25) and (12, 9)? (a) 20 (b) 28 (c) 400 (d) 21

Answer key

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

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