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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 268 · 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 (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  2. 2.In which quadrant does the point (−7, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.In which quadrant does the point (−6, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  5. 5.What is the midpoint of the line joining (0, 6) and (6, 0)? (a) (3, 4) (b) (4, 3) (c) (3, 3) (d) (6, 6)
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  7. 7.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (9, 15) and (21, 5)? (a) (30, 20) (b) (6, 5) (c) (15, 10) (d) (10, 15)
  9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  10. 10.What is the distance between the points (7, 26) and (14, 2)? (a) 625 (b) 26 (c) 31 (d) 25
  11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  12. 12.What is the distance between the points (1, 9) and (4, 5)? (a) 7 (b) 5 (c) 6 (d) 25
  13. 13.What is the distance between the points (8, 11) and (32, 4)? (a) 25 (b) 31 (c) 26 (d) 625
  14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  15. 15.What is the distance between the points (2, 7) and (10, 1)? (a) 11 (b) 14 (c) 100 (d) 10
  16. 16.In which quadrant does the point (−5, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  17. 17.What is the distance between the points (7, 14) and (19, 5)? (a) 16 (b) 21 (c) 15 (d) 225
  18. 18.In which quadrant does the point (−3, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the midpoint of the line joining (4, 6) and (12, 14)? (a) (10, 8) (b) (16, 20) (c) (4, 4) (d) (8, 10)
  20. 20.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  21. 21.In which quadrant does the point (8, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  22. 22.In which quadrant does the point (−8, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  23. 23.What is the midpoint of the line joining (9, 9) and (15, 17)? (a) (3, 4) (b) (12, 13) (c) (13, 12) (d) (24, 26)
  24. 24.What is the distance between the points (6, 16) and (12, 8)? (a) 10 (b) 100 (c) 11 (d) 14
  25. 25.What is the midpoint of the line joining (2, 11) and (4, 5)? (a) (8, 3) (b) (1, 3) (c) (3, 8) (d) (6, 16)
  26. 26.What is the midpoint of the line joining (5, 5) and (11, 9)? (a) (8, 7) (b) (3, 2) (c) (16, 14) (d) (7, 8)
  27. 27.What is the distance between the points (2, 5) and (6, 2)? (a) 5 (b) 7 (c) 6 (d) 25
  28. 28.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.What is the distance between the points (7, 15) and (15, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  30. 30.In which quadrant does the point (8, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (0, 3) and (10, 5)? (a) (10, 8) (b) (5, 4) (c) (5, 1) (d) (4, 5)
  32. 32.What is the midpoint of the line joining (1, 17) and (9, 9)? (a) (10, 26) (b) (5, 13) (c) (13, 5) (d) (4, 4)
  33. 33.In which quadrant does the point (−3, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (1, 10) and (13, 1)? (a) 15 (b) 225 (c) 16 (d) 21
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  36. 36.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  37. 37.In which quadrant does the point (−4, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.In which quadrant does the point (−6, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  39. 39.What is the midpoint of the line joining (1, 10) and (9, 2)? (a) (4, 4) (b) (5, 6) (c) (10, 12) (d) (6, 5)
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100

Answer key

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

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