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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 311 · 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 (−3, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  2. 2.What is the distance between the points (8, 9) and (20, 4)? (a) 169 (b) 13 (c) 14 (d) 17
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  4. 4.What is the distance between the points (1, 9) and (13, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  5. 5.What is the distance between the points (1, 1) and (8, 25)? (a) 26 (b) 31 (c) 25 (d) 625
  6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  7. 7.In which quadrant does the point (−1, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (3, 6) and (18, 14)? (a) 23 (b) 289 (c) 18 (d) 17
  9. 9.In which quadrant does the point (−3, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.In which quadrant does the point (−6, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  12. 12.In which quadrant does the point (9, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (2, 7) and (8, 15)? (a) (10, 22) (b) (5, 11) (c) (3, 4) (d) (11, 5)
  14. 14.In which quadrant does the point (−6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  15. 15.What is the midpoint of the line joining (7, 11) and (11, 5)? (a) (2, 3) (b) (18, 16) (c) (8, 9) (d) (9, 8)
  16. 16.What is the distance between the points (0, 5) and (8, 11)? (a) 10 (b) 100 (c) 14 (d) 11
  17. 17.What is the midpoint of the line joining (0, 6) and (6, 14)? (a) (3, 10) (b) (10, 3) (c) (3, 4) (d) (6, 20)
  18. 18.What is the distance between the points (6, 4) and (14, 10)? (a) 100 (b) 10 (c) 14 (d) 11
  19. 19.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  20. 20.What is the distance between the points (9, 2) and (21, 18)? (a) 20 (b) 400 (c) 21 (d) 28
  21. 21.What is the distance between the points (3, 28) and (10, 4)? (a) 31 (b) 26 (c) 625 (d) 25
  22. 22.What is the distance between the points (7, 16) and (23, 4)? (a) 21 (b) 28 (c) 20 (d) 400
  23. 23.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.What is the distance between the points (6, 24) and (14, 9)? (a) 23 (b) 18 (c) 289 (d) 17
  25. 25.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  26. 26.What is the distance between the points (9, 18) and (25, 6)? (a) 20 (b) 28 (c) 400 (d) 21
  27. 27.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  29. 29.What is the distance between the points (7, 5) and (19, 21)? (a) 400 (b) 21 (c) 20 (d) 28
  30. 30.What is the midpoint of the line joining (7, 12) and (19, 4)? (a) (8, 13) (b) (6, 4) (c) (13, 8) (d) (26, 16)
  31. 31.What is the midpoint of the line joining (10, 4) and (14, 2)? (a) (12, 3) (b) (2, 1) (c) (24, 6) (d) (3, 12)
  32. 32.In which quadrant does the point (5, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (0, 8) and (4, 2)? (a) (2, 5) (b) (5, 2) (c) (2, 3) (d) (4, 10)
  34. 34.What is the distance between the points (5, 13) and (8, 9)? (a) 25 (b) 5 (c) 6 (d) 7
  35. 35.What is the distance between the points (7, 7) and (31, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  37. 37.What is the midpoint of the line joining (4, 11) and (12, 7)? (a) (9, 8) (b) (16, 18) (c) (8, 9) (d) (4, 2)
  38. 38.What is the distance between the points (8, 15) and (13, 3)? (a) 169 (b) 13 (c) 14 (d) 17
  39. 39.What is the distance between the points (8, 0) and (16, 6)? (a) 14 (b) 100 (c) 11 (d) 10
  40. 40.In which quadrant does the point (6, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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